Research ArticleSurvival Models for the Analysis of Waiting Time to FirstEmployment of New Graduates A Case of 2018 Debre MarkosUniversity Graduates Northwest Ethiopia
Muluye Getie Ayaneh 1 AskalemariamAdamuDessie 2 and AmareWubishet Ayele 1
1Department of Statistics College of Natural and Computational Science Debre Markos University PO Box 269Debre Markos Ethiopia2Department of Psychology Institute of Education and Behavioral Sciences Debre Markos University Debre Markos Ethiopia
Correspondence should be addressed to Muluye Getie Ayaneh muluyegbgmailcom
Received 7 August 2020 Revised 17 September 2020 Accepted 23 September 2020 Published 23 October 2020
Academic Editor Gwo-Jen Hwang
Copyright copy 2020 Muluye Getie Ayaneh et al )is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
)is study was carried out to predict the time spell to first employment and to determine the effects of related factors on the timingof first employment on new graduates from Debre Markos University using survival models )e study used the 2018 DebreMarkos University graduate tracer survey data Cox PH and parametric accelerated failure time models were used )e Akaikeinformation criterion (AIC) was used to select the best parametric model that could explain the waiting time to first employment)e median waiting time to first employment of graduates was found to be 15 months showing that 50 of graduates managed tofind their first job 15 months after their graduation date In a comparison among parametric survival models the log-logisticparametric model was better in describing the timing of graduates to first employment Covariates such as gender cumulativegrade point average (CGPA) earned from the university age at graduation residence field of study preference of graduates andcollegefaculty were found to be statistically significant (p value lt005) predictors of the waiting time to first employment)e log-logistic parametric model fitted the waiting time to the first employment data well and could be taken as an alternative for the CoxPH model
1 Introduction
Securing a job immediately after graduation is a challengefor first-degree graduates in Ethiopia [1] A number ofuniversity graduates stay unemployed or underemployed fora longer period [2 3] )e number of students graduatingfrom universities has been increasing year by year due to themassification of students joining higher education and therapid expansion of programs in higher education [4]However despite this expansion graduate unemploymentposes a challenge to the country [5] )e countryrsquos labormarket can only absorb a limited number of graduatesthereby thousands of fresh graduates remain unemployed[2 6]
Graduate unemployment or delayed employment isattributed to the lack of soft or nontechnical skills ofgraduates poor entrepreneur skills [7ndash10] and shortage offinance to create their own jobs [6] Besides factors such asthe reputation of higher education institutions the capacityof higher education to provide consultancy service mis-match of skills between graduates and employersrsquo demandsaffect graduate employment [11] Moreover individualfactors including discipline type graduatersquos achievementgender residence family background and graduatesrsquo jobhunting skills influence graduates employment [12ndash16]
Unemployment affects not only the unemployed personbut also family members and society at large [17] )e socialand political consequences of large unemployment
HindawiEducation Research InternationalVolume 2020 Article ID 8877504 10 pageshttpsdoiorg10115520208877504
especially among educated youth can be serious [18] As aresult the issue of graduate unemployment is becoming afundamental issue that draws the attention of scholars[17 19]
Assessing the employment characteristics and theunderlying factors that influence undergraduate studentsrsquosuccessful transition into the labor market is criticalNevertheless the prevalence of unemployment and as-sociated factors in Ethiopia is not well identified anddocumented despite the efforts made by some Ethiopianpublic universities including Addis Ababa University [2]Debre Berhan University [20] and Bahir Dar University[21] Besides Batu [6] studied the determinants of youthunemployment in urban areas of Ethiopia and Reda andGebre-Eyesus [1] studied graduates and their implicationsfor unemployment in Ethiopia Cox [22] studied thesupply side factors influencing the employability of newgraduates
Nevertheless the aforementioned studies were eitherattributed to graduates in a specific field of study whichlacked inclusiveness or used inadequate statisticalmethods to explore the factors for graduateunemployment
)us the purpose of this study was to determine thepredictors related to graduatesrsquo waiting time to first em-ployment of Debre Markos University 2018 bachelorrsquosdegree graduates using survival models In this study theefficiency of two survival regression approaches Cox re-gression and parametric AFTwere compared to find out thebest model that describes the waiting time to firstemployment
2 Methodology
21 Study Population and Data Collection Procedures)is study used 2018 graduate tracer survey data from DebreMarkos University In the 2018 academic year 2716 studentsgraduated from 35 undergraduate regular programs fromDebre Markos University A total of 1105 graduates wereselected using the sampling technique suggested by Cochran[23]
)e following steps were followed to collect data from1105 graduates In the first step graduates were required tofill their baseline information such as their collegefacultyfield of study gender age cumulative grade point average(CGPA) parentsrsquo education level region where graduateswere originally from original residence and other relatedvariables immediately after their graduation date A ques-tionnaire used for data collection was taken from theEthiopian Ministry of Education prepared nationally for allEthiopian universities to conduct tracer studies with slightmodifications In the second step having spent over 16months graduates were contacted on their phone to reporttheir current situation with respect to employment statusand other related variables To do so sixteen data collectorswere recruited and trained on the data collection procedure)e information obtained from the questionnaires andtelephone interviews was entered into Excel sheets andsubsequently transferred into R software for analysis
22 Variables )e outcome variable was the time spentfrom the effective date of graduation to first employment ofgraduates (in months) Demographic and environment-related factors that are assumed as potential determinants ofwaiting time to employment of graduates to their firstemployment were used Accordingly gender (female ormale) age at graduation in years collegefaculty (CANaRMCHM IOT IEBS NCS and CBE) CGPA category resi-dence originally lived by graduates (urban or rural) edu-cational qualification achieved by either mother or father(not educated primary or secondary school and above) ifDebre Markos was graduates preference to study (yes or no)receiving training on job searching method training duringtheir stay in the university (yes or no) and if a graduatestudied hisher preferred fields of study (yes or no) wereconsidered as covariates
23 Statistical Analyses )e baseline characteristics of thestudy population were reported using descriptive statistics)e KaplanndashMeier method was used to estimate the un-employment curve Survival regression models such as CoxPH and parametric AFT were applied to assess the associ-ation between independent variables and waiting time tofirst employment upon examining different modelassumptions
231 Survival Data Analysis-e Basics In essence survivalanalysis is a statistical method for data analysis in which theoutcome variable of interest is the time to the occurrence ofan event [24] According to Orbe et al [25] the distributionof survival times is characterized by any of three functionssurvival function probability density function or the hazardfunction
Let T be a nonnegative random variable that describesthe length of time until graduate employment In our case Twould measure the duration of the first unemployment spellwhich would start when the graduate starts hisher jobsearch (T 0) and would finish when the graduate finds hisher first job (event time T t) )e survival functiondenoted by S(t) P(Tgt t) is one of the basic quantitiesemployed to describe time-to-event phenomena and isdefined as the probability of an individual being event-freeunemployed beyond time t )e hazard function (or hazardrate) specifies the instantaneous rate of failure at T tconditional upon survival to time t and is given byh(t) f(t)S(t) where f (t) is the probability densityfunction In this particular case the hazard function rep-resents the probability of finding a job at T t given that heshe has survived (has been unemployed) until t
24 Nonparametric Methods )e KaplanndashMeier (KM) es-timator which was proposed by Kaplan and Meier [26] isone of the standard nonparametric estimators of the survivalfunction (unemployment curve) S (t) )e KM estimatorproduces the waiting time to first employment curve directlyfrom the data as follows
2 Education Research International
Let rank-ordered waiting times to the first employmentare given by 0le t(1)lt t(2)lt lt t(r)leinfin then
1113954S(t)
1 if tlt t(1)
1113945j t(j)let
1 minusdj
rj
1113890 1113891 if tge t(1)
⎧⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎩
(1)
where dj is the observed number of employments at time t(j)and rj is the number of graduates who are seeking jobs attime t(j)
25 Regression Models for Survival Data
251 Cox Regression Model Cox regression (or propor-tional hazards regression) first developed by Cox in 1972 isa statistical method for investigating the effect of severalvariables on the time a specified event takes to happen [27]A multivariable Cox proportional hazards model is given bythe following equation
h t |Zi( 1113857 h0(t)exp β1z1 + β2z2 + middot middot middot + βpzp1113872 1113873
h0(t)exp Ziβ( 1113857(2)
where h(t | Z) is the hazard function that is the hazard attime t for an individual with a given specification of a set ofexplanatory variables Z which are assumed to be time-independent and h0 (t) is arbitrary the unspecified non-negative function of time known as baseline hazard whichcorresponds to the hazard when all predictor variables areequal to zero Z is the vector of covariates and β denotes thevector of the regression coefficients which is estimated usingthe partial likelihood method )e term exp(βprimeZ) dependson the covariates but not time
)e Cox regression model is a semiparametric modelwhere it makes no assumptions about the form of thenonparametric part of the model h0 (t) but assumes aparametric form for the effect of the predictors on thehazard )e main assumption of the model is the pro-portionality of hazards in that the hazard function of oneindividual is proportional to the hazard function of the otherindividual )e Cox PH model states that the factors understudy act multiplicatively on the baseline hazard functionand either increase or decrease the baseline function at aconstant rate [28] To measure the model adequacySchoenfeld residuals Cox-Snell residuals and devianceresiduals can be used
26 Parametric Methods Accelerated failure time (AFT) isan alternative to the proportional hazard (PH) model whichneeds distributional assumptions [25 29] Under AFTmodels we measure the direct effect of the explanatoryvariables on the survival time instead of the hazard as we doin the PH model )is characteristic allows for an easierinterpretation of the results because the parameters measurethe effect of the correspondent covariate on the meansurvival time [30] )e effects of the covariates in the
following equation are either to accelerate or decelerate theevent time by some constants [31]
lnT μ + αprimez + δε (3)
where αprime (α1 α2 αp) is a vector of regression coeffi-cients μ is the intercept δ is a scale parameter and ε is theerror assumed to have a particular distribution Commonchoices for the error distribution include the standardnormal distribution which yields a log-normal regressionmodel the extreme value distribution with one parameterwhich yields an exponential regression model the extremevalue distribution with two parameters which yields aWeibull regression model log-gamma which yields agamma distribution or a logistic distribution which yields alog-logistic regression model
27 Model Selection and Adequacy Akaikersquos informationcriterion (AIC) introduced by Akaike in 1973 [32] was usedto select a relatively efficient model
AIC minus2 log(L) + 2(k + c + 1) (4)
where L and K respectively are the likelihood value and thenumber of covariates of the model and c is the number ofmodel-specific distributional parameters such that in themodel c 1 for exponential and c 2 for Weibull and log-normal models )e model with a smaller AIC fits the databetter than the model with a large AIC value It can be usedto compare the adequacy of multiple probably nonnestedmodels Assessing the PH assumption for all covariates inthe Cox PH model should be an essential aspect of themodeling process when using the Cox PHmodel Hence thePH assumption of the model should be assessed to confirm ifthe ratio of hazard functions is the same at all time points Inthis study the scaled Schoenfeld residuals were analyzed tovalidate the proportional hazards assumption R statisticalsoftware version 36 forWindows was employed to carry outthe statistical analysis
3 Result
31 Descriptive Statistics At the end of the study period424 of the graduates were willing to be employed duringthe reference period but still unemployed In addition three(027) graduatesrsquo waiting times were not specified Fur-thermore 4 (03) graduates were employed even beforethey had completed their degrees
Among the graduates stated in Table 1 708 (64) ofthem were male and the remaining 397 (36) were femaleAmong the 397 female graduates who responded to theiremployment status 204 (514) secured their job whereasfrom a total of 708 male graduates 432 (61) wereemployed revealing that the percentage of unemployedfemale graduates was higher than that of male graduatesMoreover there was a statistically significant gender dif-ference regarding whether graduates are currently employed(chi-square 65 and p value 0039) As for the graduatesrsquodistribution by their cumulative grade average the majority(361) of the graduates CGPA was between 275 and 324
Education Research International 3
whereas 2852 and 55 of the graduates attained CGPA325ndash375 and 375ndash400 respectively )e remaining 297graduates scored a cumulative grade point average between 2and 274)emean age of the respondents at graduation was2385 (SD 16) years )e majority 909 (823) of thegraduates were ordinally from the Amhara region and theremaining (177) were from the other 8 regions
32 Explanatory Analysis Using Nonparametric MethodsKaplanndashMeier estimates were used to construct the survivalfunction for the waiting time to first employment FromFigure 1 the median time to first employment of graduateswas found to be 15 months which indicates that 50 of thegraduates managed to find their first job by 15 months aftertheir graduation date and the other 50 did not secure their
first job )e probability of being unemployed declinessharply fifteen months after graduation
To give a description of how graduatesrsquo unemploymentwaiting time to first employment was distributed by cova-riates KaplanndashMeier curves were drawn for covariates suchas gender college grade point average and residence ofgraduates as presented in Figure 2 Accordingly graduatesrsquocumulative grade point average (CGPA) and region of thegraduates showed considerable differences in terms of un-employment curves for each category of the covariatesrevealing that these covariates show significant differencesregarding employment of graduates For the first fifteenmonths after graduation the unemployment rate curve formales is continuously below the unemployment rate curvesof femalersquos suggesting that male graduates had significantlybetter employment than their female counterparts during
Table 1 Debre Markos University graduatesrsquo employment status by their characteristics and the p values for the log-rank test of equality ofsurvivor functions
Field of study preference Yes 364 (417) 508 (583) 003No 78 (513) 74 (487)
Study location preference Yes 318 (582) 228 (418) 079No 123 (586) 87 (414)Ever got consultancy services in theuniversity
Yes 132 (524) 120 (476) 033No 458 (614) 288 (386)Mean with standard deviation (SD) is used to summarize continuous variables frequency (n) with percentage () is used to summarize the categorical variables
4 Education Research International
the first fifteenmonths However about sixteenmonths aftergraduation the unemployment rate of females has decreasedfaster than that of males Consequently the differences
between the two curves become almost nonexistent after 16months after graduation )e unemployment curves of thegraduates are considerably different for each collegefaculty
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
Figure 1 KaplanndashMeier curve for the waiting time until the first employment
p = 00004000
025
050
075
100
Une
mpl
oym
ent r
ate
FemaleMale
Sex
Time since graduation in months0 5 10 15 20
(a)
000
025
050
075
100U
nem
ploy
men
t rat
e
p lt 00001
CGPA2ndash274275ndash324
325ndash374375ndash40
0 5 10 15 20Time since graduation in months
(b)
Time since graduation in months0 5 10 15 20
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
CollegefacultyCaNaRMCBECHMIEBS
LawNCSIOT
(c)
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
ResidenceRuralUrban
(d)
Figure 2 KaplanndashMeier curve for the waiting time for the first employment by gender college CGPA region and residence of graduatesCANaRM College of Agriculture and Natural Resource Management CHM College of Health Science and Medicine IOT Institute ofTechnology IEBS Education and Behavioral Science NCS Natural and Computational Sciences College and CBE College of Business andEconomics
Education Research International 5
that the students graduate from It is clear that fromFigure 2(c) that graduates from the health science andmedicine unemployment rate dropped faster than that of thegraduates from the remaining colleges in the study tellinggraduates from Health Science and Medicine found em-ployment much faster than the other graduates from othercollegesfaculty )e employment rate of law school grad-uates stayed constant up to 12 months after their graduationalthough it sharply dropped after 12 months of theirgraduation )is is for the fact that the majority of lawgraduates were on inductive training before they wereassigned for their first job by the government
33 Cox Proportional Hazard Model Result )e first stepconsidered in the model building procedure was to explorethe relationship between each covariate and time to em-ployment univariately Accordingly in the univariate Coxproportional hazards regression analysis age at graduation (pvalue lt0001) gender (p value lt0001) collegeinstituteschool categorization of the graduates (p value lt0001) gradepoint average (p value lt0001) the region where the graduatewere from (p value002) place of residence (p value lt0001)and field of study preference (p value 002) show a statis-tically significant association with time to first employment atthe 5 level of significance However parentrsquos educationlevels (p value 02 each) ever receiving consultancy serviceabout job hunting (p value 03245) and study area prefer-ence were found to have no significant association )emultivariable model containing all the significant covariatesin the univariable analysis is described in Table 2
34 PH Assumption Assessment and Overall Goodness-of-FitIncorporating variable(s) not satisfying the PH assumptionleads to an inferior fit of a Cox model that is the power oftest is reduced for both variables with constant and non-constant HR in the model [33] Table 3 reveals the p values ofthe tests based on the scaled Schoenfeld residuals fornonproportional hazard assessment generated by thecoxzph function survival package in R software )e resultsof the test support evidence of deviation from the pro-portionality assumption)is is because some of the p valuesfor testing whether the correlation between Schoenfeld re-sidual for these covariates and ranked survival time is lessthan 005
As a result accelerated failure time models with differentdistributional assumptions were built to model the waitingtime to first employment
35 Accelerated Failure Time Model Results Parametricmodels such as Weibull log-normal log-logistic and ex-ponential models were carried out to identify a model thatfits the data better )e summary of log-likelihood and AICis presented in Table 4 Akaikersquos information criterion (AIC)statistic for the parametric and semiparametric survivalmodels are 2191555 2194743 2188247 and 2214241 forWeibull log-normal log-logistic and exponential models
respectively )e rule is that any model that conforms to theobserved data should adequately lead to a smaller AICHence the log-logistic model appears to be with minimumAIC and BIC values among all other competing parametricmodels revealing that it is the most efficient model toidentify the predictors of the waiting time to first employ-ment of the new graduates
)e result for log-logistic which is a relatively efficientmodel is presented in Table 2 with the estimated values ofthe coefficients time ratio (TR) and its 95 CI and p valueAlthough the proportional hazard assumption was violatedthe results of the Cox PHmodel are also presented alongsidefor comparison purpose )e result of the log-logistic modelis similar to that of the hazard models in detecting thesignificant predictors of time to first employment and theirdirectional effects (positive or negative effect) However theinterpretations are not the same Nevertheless gender andfield of study preference had a statistically significant as-sociation with the waiting time for the first employmentbased on the log-logistic model at 5 level of significance butnot in the Cox PH model
)e estimate of shape parameter in the log-logistic withgamma was 063 which is less than unity suggesting thatthe probability of getting a job decreases monotonicallywith time After adjusting for other independent variablesage at graduation gender collegefaculty CGPA and placeof residence were associated with waiting time to firstemployment A predictor with a positive coefficient (timeratio or acceleration factor greater than unity) implies thatthe variables prolong the waiting time to first employmentAccordingly the acceleration factor for age was 086 (pvalue lt0001) indicating that older graduates had thetendency to have shorter waiting times until first em-ployment )e median waiting time for males was 082times lower than that of females As for the CGPA earnedfrom the university it was found that compared to theinterval of 374ndash40 CGPA receivers graduates who earnedCGPA in 324ndash375 range have to wait 131 times (p value
009) and 275ndash324 graders have to wait 171 times (p valuelt0001) while low achiever (20ndash274) graduates have towait 232 times (p value lt0001) longer When comparinggraduates who were ordinally from urban areas to thosewho were from rural those who were from rural areas hadto wait 215 times (p value lt0001) longer to find their firstjob revealing that graduates from urban areas had shorterwaiting time to first employment compared to those fromrural areas
)ose graduates from all colleges had longer waitingtimes for first employment as compared to the college ofhealth science and medicine However the difference in thewaiting time of first employment between school of law andcollege of health science and medicine is not statisticallysignificant (TR 071 p value 03) )e results in Table 2also show that the median waiting time until first em-ployment for graduates who studied their preferred fieldswas 08 times (p value 0049) shorter than that of graduateswho did not study their preferred fields
6 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
especially among educated youth can be serious [18] As aresult the issue of graduate unemployment is becoming afundamental issue that draws the attention of scholars[17 19]
Assessing the employment characteristics and theunderlying factors that influence undergraduate studentsrsquosuccessful transition into the labor market is criticalNevertheless the prevalence of unemployment and as-sociated factors in Ethiopia is not well identified anddocumented despite the efforts made by some Ethiopianpublic universities including Addis Ababa University [2]Debre Berhan University [20] and Bahir Dar University[21] Besides Batu [6] studied the determinants of youthunemployment in urban areas of Ethiopia and Reda andGebre-Eyesus [1] studied graduates and their implicationsfor unemployment in Ethiopia Cox [22] studied thesupply side factors influencing the employability of newgraduates
Nevertheless the aforementioned studies were eitherattributed to graduates in a specific field of study whichlacked inclusiveness or used inadequate statisticalmethods to explore the factors for graduateunemployment
)us the purpose of this study was to determine thepredictors related to graduatesrsquo waiting time to first em-ployment of Debre Markos University 2018 bachelorrsquosdegree graduates using survival models In this study theefficiency of two survival regression approaches Cox re-gression and parametric AFTwere compared to find out thebest model that describes the waiting time to firstemployment
2 Methodology
21 Study Population and Data Collection Procedures)is study used 2018 graduate tracer survey data from DebreMarkos University In the 2018 academic year 2716 studentsgraduated from 35 undergraduate regular programs fromDebre Markos University A total of 1105 graduates wereselected using the sampling technique suggested by Cochran[23]
)e following steps were followed to collect data from1105 graduates In the first step graduates were required tofill their baseline information such as their collegefacultyfield of study gender age cumulative grade point average(CGPA) parentsrsquo education level region where graduateswere originally from original residence and other relatedvariables immediately after their graduation date A ques-tionnaire used for data collection was taken from theEthiopian Ministry of Education prepared nationally for allEthiopian universities to conduct tracer studies with slightmodifications In the second step having spent over 16months graduates were contacted on their phone to reporttheir current situation with respect to employment statusand other related variables To do so sixteen data collectorswere recruited and trained on the data collection procedure)e information obtained from the questionnaires andtelephone interviews was entered into Excel sheets andsubsequently transferred into R software for analysis
22 Variables )e outcome variable was the time spentfrom the effective date of graduation to first employment ofgraduates (in months) Demographic and environment-related factors that are assumed as potential determinants ofwaiting time to employment of graduates to their firstemployment were used Accordingly gender (female ormale) age at graduation in years collegefaculty (CANaRMCHM IOT IEBS NCS and CBE) CGPA category resi-dence originally lived by graduates (urban or rural) edu-cational qualification achieved by either mother or father(not educated primary or secondary school and above) ifDebre Markos was graduates preference to study (yes or no)receiving training on job searching method training duringtheir stay in the university (yes or no) and if a graduatestudied hisher preferred fields of study (yes or no) wereconsidered as covariates
23 Statistical Analyses )e baseline characteristics of thestudy population were reported using descriptive statistics)e KaplanndashMeier method was used to estimate the un-employment curve Survival regression models such as CoxPH and parametric AFT were applied to assess the associ-ation between independent variables and waiting time tofirst employment upon examining different modelassumptions
231 Survival Data Analysis-e Basics In essence survivalanalysis is a statistical method for data analysis in which theoutcome variable of interest is the time to the occurrence ofan event [24] According to Orbe et al [25] the distributionof survival times is characterized by any of three functionssurvival function probability density function or the hazardfunction
Let T be a nonnegative random variable that describesthe length of time until graduate employment In our case Twould measure the duration of the first unemployment spellwhich would start when the graduate starts hisher jobsearch (T 0) and would finish when the graduate finds hisher first job (event time T t) )e survival functiondenoted by S(t) P(Tgt t) is one of the basic quantitiesemployed to describe time-to-event phenomena and isdefined as the probability of an individual being event-freeunemployed beyond time t )e hazard function (or hazardrate) specifies the instantaneous rate of failure at T tconditional upon survival to time t and is given byh(t) f(t)S(t) where f (t) is the probability densityfunction In this particular case the hazard function rep-resents the probability of finding a job at T t given that heshe has survived (has been unemployed) until t
24 Nonparametric Methods )e KaplanndashMeier (KM) es-timator which was proposed by Kaplan and Meier [26] isone of the standard nonparametric estimators of the survivalfunction (unemployment curve) S (t) )e KM estimatorproduces the waiting time to first employment curve directlyfrom the data as follows
2 Education Research International
Let rank-ordered waiting times to the first employmentare given by 0le t(1)lt t(2)lt lt t(r)leinfin then
1113954S(t)
1 if tlt t(1)
1113945j t(j)let
1 minusdj
rj
1113890 1113891 if tge t(1)
⎧⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎩
(1)
where dj is the observed number of employments at time t(j)and rj is the number of graduates who are seeking jobs attime t(j)
25 Regression Models for Survival Data
251 Cox Regression Model Cox regression (or propor-tional hazards regression) first developed by Cox in 1972 isa statistical method for investigating the effect of severalvariables on the time a specified event takes to happen [27]A multivariable Cox proportional hazards model is given bythe following equation
h t |Zi( 1113857 h0(t)exp β1z1 + β2z2 + middot middot middot + βpzp1113872 1113873
h0(t)exp Ziβ( 1113857(2)
where h(t | Z) is the hazard function that is the hazard attime t for an individual with a given specification of a set ofexplanatory variables Z which are assumed to be time-independent and h0 (t) is arbitrary the unspecified non-negative function of time known as baseline hazard whichcorresponds to the hazard when all predictor variables areequal to zero Z is the vector of covariates and β denotes thevector of the regression coefficients which is estimated usingthe partial likelihood method )e term exp(βprimeZ) dependson the covariates but not time
)e Cox regression model is a semiparametric modelwhere it makes no assumptions about the form of thenonparametric part of the model h0 (t) but assumes aparametric form for the effect of the predictors on thehazard )e main assumption of the model is the pro-portionality of hazards in that the hazard function of oneindividual is proportional to the hazard function of the otherindividual )e Cox PH model states that the factors understudy act multiplicatively on the baseline hazard functionand either increase or decrease the baseline function at aconstant rate [28] To measure the model adequacySchoenfeld residuals Cox-Snell residuals and devianceresiduals can be used
26 Parametric Methods Accelerated failure time (AFT) isan alternative to the proportional hazard (PH) model whichneeds distributional assumptions [25 29] Under AFTmodels we measure the direct effect of the explanatoryvariables on the survival time instead of the hazard as we doin the PH model )is characteristic allows for an easierinterpretation of the results because the parameters measurethe effect of the correspondent covariate on the meansurvival time [30] )e effects of the covariates in the
following equation are either to accelerate or decelerate theevent time by some constants [31]
lnT μ + αprimez + δε (3)
where αprime (α1 α2 αp) is a vector of regression coeffi-cients μ is the intercept δ is a scale parameter and ε is theerror assumed to have a particular distribution Commonchoices for the error distribution include the standardnormal distribution which yields a log-normal regressionmodel the extreme value distribution with one parameterwhich yields an exponential regression model the extremevalue distribution with two parameters which yields aWeibull regression model log-gamma which yields agamma distribution or a logistic distribution which yields alog-logistic regression model
27 Model Selection and Adequacy Akaikersquos informationcriterion (AIC) introduced by Akaike in 1973 [32] was usedto select a relatively efficient model
AIC minus2 log(L) + 2(k + c + 1) (4)
where L and K respectively are the likelihood value and thenumber of covariates of the model and c is the number ofmodel-specific distributional parameters such that in themodel c 1 for exponential and c 2 for Weibull and log-normal models )e model with a smaller AIC fits the databetter than the model with a large AIC value It can be usedto compare the adequacy of multiple probably nonnestedmodels Assessing the PH assumption for all covariates inthe Cox PH model should be an essential aspect of themodeling process when using the Cox PHmodel Hence thePH assumption of the model should be assessed to confirm ifthe ratio of hazard functions is the same at all time points Inthis study the scaled Schoenfeld residuals were analyzed tovalidate the proportional hazards assumption R statisticalsoftware version 36 forWindows was employed to carry outthe statistical analysis
3 Result
31 Descriptive Statistics At the end of the study period424 of the graduates were willing to be employed duringthe reference period but still unemployed In addition three(027) graduatesrsquo waiting times were not specified Fur-thermore 4 (03) graduates were employed even beforethey had completed their degrees
Among the graduates stated in Table 1 708 (64) ofthem were male and the remaining 397 (36) were femaleAmong the 397 female graduates who responded to theiremployment status 204 (514) secured their job whereasfrom a total of 708 male graduates 432 (61) wereemployed revealing that the percentage of unemployedfemale graduates was higher than that of male graduatesMoreover there was a statistically significant gender dif-ference regarding whether graduates are currently employed(chi-square 65 and p value 0039) As for the graduatesrsquodistribution by their cumulative grade average the majority(361) of the graduates CGPA was between 275 and 324
Education Research International 3
whereas 2852 and 55 of the graduates attained CGPA325ndash375 and 375ndash400 respectively )e remaining 297graduates scored a cumulative grade point average between 2and 274)emean age of the respondents at graduation was2385 (SD 16) years )e majority 909 (823) of thegraduates were ordinally from the Amhara region and theremaining (177) were from the other 8 regions
32 Explanatory Analysis Using Nonparametric MethodsKaplanndashMeier estimates were used to construct the survivalfunction for the waiting time to first employment FromFigure 1 the median time to first employment of graduateswas found to be 15 months which indicates that 50 of thegraduates managed to find their first job by 15 months aftertheir graduation date and the other 50 did not secure their
first job )e probability of being unemployed declinessharply fifteen months after graduation
To give a description of how graduatesrsquo unemploymentwaiting time to first employment was distributed by cova-riates KaplanndashMeier curves were drawn for covariates suchas gender college grade point average and residence ofgraduates as presented in Figure 2 Accordingly graduatesrsquocumulative grade point average (CGPA) and region of thegraduates showed considerable differences in terms of un-employment curves for each category of the covariatesrevealing that these covariates show significant differencesregarding employment of graduates For the first fifteenmonths after graduation the unemployment rate curve formales is continuously below the unemployment rate curvesof femalersquos suggesting that male graduates had significantlybetter employment than their female counterparts during
Table 1 Debre Markos University graduatesrsquo employment status by their characteristics and the p values for the log-rank test of equality ofsurvivor functions
Field of study preference Yes 364 (417) 508 (583) 003No 78 (513) 74 (487)
Study location preference Yes 318 (582) 228 (418) 079No 123 (586) 87 (414)Ever got consultancy services in theuniversity
Yes 132 (524) 120 (476) 033No 458 (614) 288 (386)Mean with standard deviation (SD) is used to summarize continuous variables frequency (n) with percentage () is used to summarize the categorical variables
4 Education Research International
the first fifteenmonths However about sixteenmonths aftergraduation the unemployment rate of females has decreasedfaster than that of males Consequently the differences
between the two curves become almost nonexistent after 16months after graduation )e unemployment curves of thegraduates are considerably different for each collegefaculty
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
Figure 1 KaplanndashMeier curve for the waiting time until the first employment
p = 00004000
025
050
075
100
Une
mpl
oym
ent r
ate
FemaleMale
Sex
Time since graduation in months0 5 10 15 20
(a)
000
025
050
075
100U
nem
ploy
men
t rat
e
p lt 00001
CGPA2ndash274275ndash324
325ndash374375ndash40
0 5 10 15 20Time since graduation in months
(b)
Time since graduation in months0 5 10 15 20
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
CollegefacultyCaNaRMCBECHMIEBS
LawNCSIOT
(c)
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
ResidenceRuralUrban
(d)
Figure 2 KaplanndashMeier curve for the waiting time for the first employment by gender college CGPA region and residence of graduatesCANaRM College of Agriculture and Natural Resource Management CHM College of Health Science and Medicine IOT Institute ofTechnology IEBS Education and Behavioral Science NCS Natural and Computational Sciences College and CBE College of Business andEconomics
Education Research International 5
that the students graduate from It is clear that fromFigure 2(c) that graduates from the health science andmedicine unemployment rate dropped faster than that of thegraduates from the remaining colleges in the study tellinggraduates from Health Science and Medicine found em-ployment much faster than the other graduates from othercollegesfaculty )e employment rate of law school grad-uates stayed constant up to 12 months after their graduationalthough it sharply dropped after 12 months of theirgraduation )is is for the fact that the majority of lawgraduates were on inductive training before they wereassigned for their first job by the government
33 Cox Proportional Hazard Model Result )e first stepconsidered in the model building procedure was to explorethe relationship between each covariate and time to em-ployment univariately Accordingly in the univariate Coxproportional hazards regression analysis age at graduation (pvalue lt0001) gender (p value lt0001) collegeinstituteschool categorization of the graduates (p value lt0001) gradepoint average (p value lt0001) the region where the graduatewere from (p value002) place of residence (p value lt0001)and field of study preference (p value 002) show a statis-tically significant association with time to first employment atthe 5 level of significance However parentrsquos educationlevels (p value 02 each) ever receiving consultancy serviceabout job hunting (p value 03245) and study area prefer-ence were found to have no significant association )emultivariable model containing all the significant covariatesin the univariable analysis is described in Table 2
34 PH Assumption Assessment and Overall Goodness-of-FitIncorporating variable(s) not satisfying the PH assumptionleads to an inferior fit of a Cox model that is the power oftest is reduced for both variables with constant and non-constant HR in the model [33] Table 3 reveals the p values ofthe tests based on the scaled Schoenfeld residuals fornonproportional hazard assessment generated by thecoxzph function survival package in R software )e resultsof the test support evidence of deviation from the pro-portionality assumption)is is because some of the p valuesfor testing whether the correlation between Schoenfeld re-sidual for these covariates and ranked survival time is lessthan 005
As a result accelerated failure time models with differentdistributional assumptions were built to model the waitingtime to first employment
35 Accelerated Failure Time Model Results Parametricmodels such as Weibull log-normal log-logistic and ex-ponential models were carried out to identify a model thatfits the data better )e summary of log-likelihood and AICis presented in Table 4 Akaikersquos information criterion (AIC)statistic for the parametric and semiparametric survivalmodels are 2191555 2194743 2188247 and 2214241 forWeibull log-normal log-logistic and exponential models
respectively )e rule is that any model that conforms to theobserved data should adequately lead to a smaller AICHence the log-logistic model appears to be with minimumAIC and BIC values among all other competing parametricmodels revealing that it is the most efficient model toidentify the predictors of the waiting time to first employ-ment of the new graduates
)e result for log-logistic which is a relatively efficientmodel is presented in Table 2 with the estimated values ofthe coefficients time ratio (TR) and its 95 CI and p valueAlthough the proportional hazard assumption was violatedthe results of the Cox PHmodel are also presented alongsidefor comparison purpose )e result of the log-logistic modelis similar to that of the hazard models in detecting thesignificant predictors of time to first employment and theirdirectional effects (positive or negative effect) However theinterpretations are not the same Nevertheless gender andfield of study preference had a statistically significant as-sociation with the waiting time for the first employmentbased on the log-logistic model at 5 level of significance butnot in the Cox PH model
)e estimate of shape parameter in the log-logistic withgamma was 063 which is less than unity suggesting thatthe probability of getting a job decreases monotonicallywith time After adjusting for other independent variablesage at graduation gender collegefaculty CGPA and placeof residence were associated with waiting time to firstemployment A predictor with a positive coefficient (timeratio or acceleration factor greater than unity) implies thatthe variables prolong the waiting time to first employmentAccordingly the acceleration factor for age was 086 (pvalue lt0001) indicating that older graduates had thetendency to have shorter waiting times until first em-ployment )e median waiting time for males was 082times lower than that of females As for the CGPA earnedfrom the university it was found that compared to theinterval of 374ndash40 CGPA receivers graduates who earnedCGPA in 324ndash375 range have to wait 131 times (p value
009) and 275ndash324 graders have to wait 171 times (p valuelt0001) while low achiever (20ndash274) graduates have towait 232 times (p value lt0001) longer When comparinggraduates who were ordinally from urban areas to thosewho were from rural those who were from rural areas hadto wait 215 times (p value lt0001) longer to find their firstjob revealing that graduates from urban areas had shorterwaiting time to first employment compared to those fromrural areas
)ose graduates from all colleges had longer waitingtimes for first employment as compared to the college ofhealth science and medicine However the difference in thewaiting time of first employment between school of law andcollege of health science and medicine is not statisticallysignificant (TR 071 p value 03) )e results in Table 2also show that the median waiting time until first em-ployment for graduates who studied their preferred fieldswas 08 times (p value 0049) shorter than that of graduateswho did not study their preferred fields
6 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
Let rank-ordered waiting times to the first employmentare given by 0le t(1)lt t(2)lt lt t(r)leinfin then
1113954S(t)
1 if tlt t(1)
1113945j t(j)let
1 minusdj
rj
1113890 1113891 if tge t(1)
⎧⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎩
(1)
where dj is the observed number of employments at time t(j)and rj is the number of graduates who are seeking jobs attime t(j)
25 Regression Models for Survival Data
251 Cox Regression Model Cox regression (or propor-tional hazards regression) first developed by Cox in 1972 isa statistical method for investigating the effect of severalvariables on the time a specified event takes to happen [27]A multivariable Cox proportional hazards model is given bythe following equation
h t |Zi( 1113857 h0(t)exp β1z1 + β2z2 + middot middot middot + βpzp1113872 1113873
h0(t)exp Ziβ( 1113857(2)
where h(t | Z) is the hazard function that is the hazard attime t for an individual with a given specification of a set ofexplanatory variables Z which are assumed to be time-independent and h0 (t) is arbitrary the unspecified non-negative function of time known as baseline hazard whichcorresponds to the hazard when all predictor variables areequal to zero Z is the vector of covariates and β denotes thevector of the regression coefficients which is estimated usingthe partial likelihood method )e term exp(βprimeZ) dependson the covariates but not time
)e Cox regression model is a semiparametric modelwhere it makes no assumptions about the form of thenonparametric part of the model h0 (t) but assumes aparametric form for the effect of the predictors on thehazard )e main assumption of the model is the pro-portionality of hazards in that the hazard function of oneindividual is proportional to the hazard function of the otherindividual )e Cox PH model states that the factors understudy act multiplicatively on the baseline hazard functionand either increase or decrease the baseline function at aconstant rate [28] To measure the model adequacySchoenfeld residuals Cox-Snell residuals and devianceresiduals can be used
26 Parametric Methods Accelerated failure time (AFT) isan alternative to the proportional hazard (PH) model whichneeds distributional assumptions [25 29] Under AFTmodels we measure the direct effect of the explanatoryvariables on the survival time instead of the hazard as we doin the PH model )is characteristic allows for an easierinterpretation of the results because the parameters measurethe effect of the correspondent covariate on the meansurvival time [30] )e effects of the covariates in the
following equation are either to accelerate or decelerate theevent time by some constants [31]
lnT μ + αprimez + δε (3)
where αprime (α1 α2 αp) is a vector of regression coeffi-cients μ is the intercept δ is a scale parameter and ε is theerror assumed to have a particular distribution Commonchoices for the error distribution include the standardnormal distribution which yields a log-normal regressionmodel the extreme value distribution with one parameterwhich yields an exponential regression model the extremevalue distribution with two parameters which yields aWeibull regression model log-gamma which yields agamma distribution or a logistic distribution which yields alog-logistic regression model
27 Model Selection and Adequacy Akaikersquos informationcriterion (AIC) introduced by Akaike in 1973 [32] was usedto select a relatively efficient model
AIC minus2 log(L) + 2(k + c + 1) (4)
where L and K respectively are the likelihood value and thenumber of covariates of the model and c is the number ofmodel-specific distributional parameters such that in themodel c 1 for exponential and c 2 for Weibull and log-normal models )e model with a smaller AIC fits the databetter than the model with a large AIC value It can be usedto compare the adequacy of multiple probably nonnestedmodels Assessing the PH assumption for all covariates inthe Cox PH model should be an essential aspect of themodeling process when using the Cox PHmodel Hence thePH assumption of the model should be assessed to confirm ifthe ratio of hazard functions is the same at all time points Inthis study the scaled Schoenfeld residuals were analyzed tovalidate the proportional hazards assumption R statisticalsoftware version 36 forWindows was employed to carry outthe statistical analysis
3 Result
31 Descriptive Statistics At the end of the study period424 of the graduates were willing to be employed duringthe reference period but still unemployed In addition three(027) graduatesrsquo waiting times were not specified Fur-thermore 4 (03) graduates were employed even beforethey had completed their degrees
Among the graduates stated in Table 1 708 (64) ofthem were male and the remaining 397 (36) were femaleAmong the 397 female graduates who responded to theiremployment status 204 (514) secured their job whereasfrom a total of 708 male graduates 432 (61) wereemployed revealing that the percentage of unemployedfemale graduates was higher than that of male graduatesMoreover there was a statistically significant gender dif-ference regarding whether graduates are currently employed(chi-square 65 and p value 0039) As for the graduatesrsquodistribution by their cumulative grade average the majority(361) of the graduates CGPA was between 275 and 324
Education Research International 3
whereas 2852 and 55 of the graduates attained CGPA325ndash375 and 375ndash400 respectively )e remaining 297graduates scored a cumulative grade point average between 2and 274)emean age of the respondents at graduation was2385 (SD 16) years )e majority 909 (823) of thegraduates were ordinally from the Amhara region and theremaining (177) were from the other 8 regions
32 Explanatory Analysis Using Nonparametric MethodsKaplanndashMeier estimates were used to construct the survivalfunction for the waiting time to first employment FromFigure 1 the median time to first employment of graduateswas found to be 15 months which indicates that 50 of thegraduates managed to find their first job by 15 months aftertheir graduation date and the other 50 did not secure their
first job )e probability of being unemployed declinessharply fifteen months after graduation
To give a description of how graduatesrsquo unemploymentwaiting time to first employment was distributed by cova-riates KaplanndashMeier curves were drawn for covariates suchas gender college grade point average and residence ofgraduates as presented in Figure 2 Accordingly graduatesrsquocumulative grade point average (CGPA) and region of thegraduates showed considerable differences in terms of un-employment curves for each category of the covariatesrevealing that these covariates show significant differencesregarding employment of graduates For the first fifteenmonths after graduation the unemployment rate curve formales is continuously below the unemployment rate curvesof femalersquos suggesting that male graduates had significantlybetter employment than their female counterparts during
Table 1 Debre Markos University graduatesrsquo employment status by their characteristics and the p values for the log-rank test of equality ofsurvivor functions
Field of study preference Yes 364 (417) 508 (583) 003No 78 (513) 74 (487)
Study location preference Yes 318 (582) 228 (418) 079No 123 (586) 87 (414)Ever got consultancy services in theuniversity
Yes 132 (524) 120 (476) 033No 458 (614) 288 (386)Mean with standard deviation (SD) is used to summarize continuous variables frequency (n) with percentage () is used to summarize the categorical variables
4 Education Research International
the first fifteenmonths However about sixteenmonths aftergraduation the unemployment rate of females has decreasedfaster than that of males Consequently the differences
between the two curves become almost nonexistent after 16months after graduation )e unemployment curves of thegraduates are considerably different for each collegefaculty
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
Figure 1 KaplanndashMeier curve for the waiting time until the first employment
p = 00004000
025
050
075
100
Une
mpl
oym
ent r
ate
FemaleMale
Sex
Time since graduation in months0 5 10 15 20
(a)
000
025
050
075
100U
nem
ploy
men
t rat
e
p lt 00001
CGPA2ndash274275ndash324
325ndash374375ndash40
0 5 10 15 20Time since graduation in months
(b)
Time since graduation in months0 5 10 15 20
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
CollegefacultyCaNaRMCBECHMIEBS
LawNCSIOT
(c)
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
ResidenceRuralUrban
(d)
Figure 2 KaplanndashMeier curve for the waiting time for the first employment by gender college CGPA region and residence of graduatesCANaRM College of Agriculture and Natural Resource Management CHM College of Health Science and Medicine IOT Institute ofTechnology IEBS Education and Behavioral Science NCS Natural and Computational Sciences College and CBE College of Business andEconomics
Education Research International 5
that the students graduate from It is clear that fromFigure 2(c) that graduates from the health science andmedicine unemployment rate dropped faster than that of thegraduates from the remaining colleges in the study tellinggraduates from Health Science and Medicine found em-ployment much faster than the other graduates from othercollegesfaculty )e employment rate of law school grad-uates stayed constant up to 12 months after their graduationalthough it sharply dropped after 12 months of theirgraduation )is is for the fact that the majority of lawgraduates were on inductive training before they wereassigned for their first job by the government
33 Cox Proportional Hazard Model Result )e first stepconsidered in the model building procedure was to explorethe relationship between each covariate and time to em-ployment univariately Accordingly in the univariate Coxproportional hazards regression analysis age at graduation (pvalue lt0001) gender (p value lt0001) collegeinstituteschool categorization of the graduates (p value lt0001) gradepoint average (p value lt0001) the region where the graduatewere from (p value002) place of residence (p value lt0001)and field of study preference (p value 002) show a statis-tically significant association with time to first employment atthe 5 level of significance However parentrsquos educationlevels (p value 02 each) ever receiving consultancy serviceabout job hunting (p value 03245) and study area prefer-ence were found to have no significant association )emultivariable model containing all the significant covariatesin the univariable analysis is described in Table 2
34 PH Assumption Assessment and Overall Goodness-of-FitIncorporating variable(s) not satisfying the PH assumptionleads to an inferior fit of a Cox model that is the power oftest is reduced for both variables with constant and non-constant HR in the model [33] Table 3 reveals the p values ofthe tests based on the scaled Schoenfeld residuals fornonproportional hazard assessment generated by thecoxzph function survival package in R software )e resultsof the test support evidence of deviation from the pro-portionality assumption)is is because some of the p valuesfor testing whether the correlation between Schoenfeld re-sidual for these covariates and ranked survival time is lessthan 005
As a result accelerated failure time models with differentdistributional assumptions were built to model the waitingtime to first employment
35 Accelerated Failure Time Model Results Parametricmodels such as Weibull log-normal log-logistic and ex-ponential models were carried out to identify a model thatfits the data better )e summary of log-likelihood and AICis presented in Table 4 Akaikersquos information criterion (AIC)statistic for the parametric and semiparametric survivalmodels are 2191555 2194743 2188247 and 2214241 forWeibull log-normal log-logistic and exponential models
respectively )e rule is that any model that conforms to theobserved data should adequately lead to a smaller AICHence the log-logistic model appears to be with minimumAIC and BIC values among all other competing parametricmodels revealing that it is the most efficient model toidentify the predictors of the waiting time to first employ-ment of the new graduates
)e result for log-logistic which is a relatively efficientmodel is presented in Table 2 with the estimated values ofthe coefficients time ratio (TR) and its 95 CI and p valueAlthough the proportional hazard assumption was violatedthe results of the Cox PHmodel are also presented alongsidefor comparison purpose )e result of the log-logistic modelis similar to that of the hazard models in detecting thesignificant predictors of time to first employment and theirdirectional effects (positive or negative effect) However theinterpretations are not the same Nevertheless gender andfield of study preference had a statistically significant as-sociation with the waiting time for the first employmentbased on the log-logistic model at 5 level of significance butnot in the Cox PH model
)e estimate of shape parameter in the log-logistic withgamma was 063 which is less than unity suggesting thatthe probability of getting a job decreases monotonicallywith time After adjusting for other independent variablesage at graduation gender collegefaculty CGPA and placeof residence were associated with waiting time to firstemployment A predictor with a positive coefficient (timeratio or acceleration factor greater than unity) implies thatthe variables prolong the waiting time to first employmentAccordingly the acceleration factor for age was 086 (pvalue lt0001) indicating that older graduates had thetendency to have shorter waiting times until first em-ployment )e median waiting time for males was 082times lower than that of females As for the CGPA earnedfrom the university it was found that compared to theinterval of 374ndash40 CGPA receivers graduates who earnedCGPA in 324ndash375 range have to wait 131 times (p value
009) and 275ndash324 graders have to wait 171 times (p valuelt0001) while low achiever (20ndash274) graduates have towait 232 times (p value lt0001) longer When comparinggraduates who were ordinally from urban areas to thosewho were from rural those who were from rural areas hadto wait 215 times (p value lt0001) longer to find their firstjob revealing that graduates from urban areas had shorterwaiting time to first employment compared to those fromrural areas
)ose graduates from all colleges had longer waitingtimes for first employment as compared to the college ofhealth science and medicine However the difference in thewaiting time of first employment between school of law andcollege of health science and medicine is not statisticallysignificant (TR 071 p value 03) )e results in Table 2also show that the median waiting time until first em-ployment for graduates who studied their preferred fieldswas 08 times (p value 0049) shorter than that of graduateswho did not study their preferred fields
6 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
whereas 2852 and 55 of the graduates attained CGPA325ndash375 and 375ndash400 respectively )e remaining 297graduates scored a cumulative grade point average between 2and 274)emean age of the respondents at graduation was2385 (SD 16) years )e majority 909 (823) of thegraduates were ordinally from the Amhara region and theremaining (177) were from the other 8 regions
32 Explanatory Analysis Using Nonparametric MethodsKaplanndashMeier estimates were used to construct the survivalfunction for the waiting time to first employment FromFigure 1 the median time to first employment of graduateswas found to be 15 months which indicates that 50 of thegraduates managed to find their first job by 15 months aftertheir graduation date and the other 50 did not secure their
first job )e probability of being unemployed declinessharply fifteen months after graduation
To give a description of how graduatesrsquo unemploymentwaiting time to first employment was distributed by cova-riates KaplanndashMeier curves were drawn for covariates suchas gender college grade point average and residence ofgraduates as presented in Figure 2 Accordingly graduatesrsquocumulative grade point average (CGPA) and region of thegraduates showed considerable differences in terms of un-employment curves for each category of the covariatesrevealing that these covariates show significant differencesregarding employment of graduates For the first fifteenmonths after graduation the unemployment rate curve formales is continuously below the unemployment rate curvesof femalersquos suggesting that male graduates had significantlybetter employment than their female counterparts during
Table 1 Debre Markos University graduatesrsquo employment status by their characteristics and the p values for the log-rank test of equality ofsurvivor functions
Field of study preference Yes 364 (417) 508 (583) 003No 78 (513) 74 (487)
Study location preference Yes 318 (582) 228 (418) 079No 123 (586) 87 (414)Ever got consultancy services in theuniversity
Yes 132 (524) 120 (476) 033No 458 (614) 288 (386)Mean with standard deviation (SD) is used to summarize continuous variables frequency (n) with percentage () is used to summarize the categorical variables
4 Education Research International
the first fifteenmonths However about sixteenmonths aftergraduation the unemployment rate of females has decreasedfaster than that of males Consequently the differences
between the two curves become almost nonexistent after 16months after graduation )e unemployment curves of thegraduates are considerably different for each collegefaculty
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
Figure 1 KaplanndashMeier curve for the waiting time until the first employment
p = 00004000
025
050
075
100
Une
mpl
oym
ent r
ate
FemaleMale
Sex
Time since graduation in months0 5 10 15 20
(a)
000
025
050
075
100U
nem
ploy
men
t rat
e
p lt 00001
CGPA2ndash274275ndash324
325ndash374375ndash40
0 5 10 15 20Time since graduation in months
(b)
Time since graduation in months0 5 10 15 20
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
CollegefacultyCaNaRMCBECHMIEBS
LawNCSIOT
(c)
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
ResidenceRuralUrban
(d)
Figure 2 KaplanndashMeier curve for the waiting time for the first employment by gender college CGPA region and residence of graduatesCANaRM College of Agriculture and Natural Resource Management CHM College of Health Science and Medicine IOT Institute ofTechnology IEBS Education and Behavioral Science NCS Natural and Computational Sciences College and CBE College of Business andEconomics
Education Research International 5
that the students graduate from It is clear that fromFigure 2(c) that graduates from the health science andmedicine unemployment rate dropped faster than that of thegraduates from the remaining colleges in the study tellinggraduates from Health Science and Medicine found em-ployment much faster than the other graduates from othercollegesfaculty )e employment rate of law school grad-uates stayed constant up to 12 months after their graduationalthough it sharply dropped after 12 months of theirgraduation )is is for the fact that the majority of lawgraduates were on inductive training before they wereassigned for their first job by the government
33 Cox Proportional Hazard Model Result )e first stepconsidered in the model building procedure was to explorethe relationship between each covariate and time to em-ployment univariately Accordingly in the univariate Coxproportional hazards regression analysis age at graduation (pvalue lt0001) gender (p value lt0001) collegeinstituteschool categorization of the graduates (p value lt0001) gradepoint average (p value lt0001) the region where the graduatewere from (p value002) place of residence (p value lt0001)and field of study preference (p value 002) show a statis-tically significant association with time to first employment atthe 5 level of significance However parentrsquos educationlevels (p value 02 each) ever receiving consultancy serviceabout job hunting (p value 03245) and study area prefer-ence were found to have no significant association )emultivariable model containing all the significant covariatesin the univariable analysis is described in Table 2
34 PH Assumption Assessment and Overall Goodness-of-FitIncorporating variable(s) not satisfying the PH assumptionleads to an inferior fit of a Cox model that is the power oftest is reduced for both variables with constant and non-constant HR in the model [33] Table 3 reveals the p values ofthe tests based on the scaled Schoenfeld residuals fornonproportional hazard assessment generated by thecoxzph function survival package in R software )e resultsof the test support evidence of deviation from the pro-portionality assumption)is is because some of the p valuesfor testing whether the correlation between Schoenfeld re-sidual for these covariates and ranked survival time is lessthan 005
As a result accelerated failure time models with differentdistributional assumptions were built to model the waitingtime to first employment
35 Accelerated Failure Time Model Results Parametricmodels such as Weibull log-normal log-logistic and ex-ponential models were carried out to identify a model thatfits the data better )e summary of log-likelihood and AICis presented in Table 4 Akaikersquos information criterion (AIC)statistic for the parametric and semiparametric survivalmodels are 2191555 2194743 2188247 and 2214241 forWeibull log-normal log-logistic and exponential models
respectively )e rule is that any model that conforms to theobserved data should adequately lead to a smaller AICHence the log-logistic model appears to be with minimumAIC and BIC values among all other competing parametricmodels revealing that it is the most efficient model toidentify the predictors of the waiting time to first employ-ment of the new graduates
)e result for log-logistic which is a relatively efficientmodel is presented in Table 2 with the estimated values ofthe coefficients time ratio (TR) and its 95 CI and p valueAlthough the proportional hazard assumption was violatedthe results of the Cox PHmodel are also presented alongsidefor comparison purpose )e result of the log-logistic modelis similar to that of the hazard models in detecting thesignificant predictors of time to first employment and theirdirectional effects (positive or negative effect) However theinterpretations are not the same Nevertheless gender andfield of study preference had a statistically significant as-sociation with the waiting time for the first employmentbased on the log-logistic model at 5 level of significance butnot in the Cox PH model
)e estimate of shape parameter in the log-logistic withgamma was 063 which is less than unity suggesting thatthe probability of getting a job decreases monotonicallywith time After adjusting for other independent variablesage at graduation gender collegefaculty CGPA and placeof residence were associated with waiting time to firstemployment A predictor with a positive coefficient (timeratio or acceleration factor greater than unity) implies thatthe variables prolong the waiting time to first employmentAccordingly the acceleration factor for age was 086 (pvalue lt0001) indicating that older graduates had thetendency to have shorter waiting times until first em-ployment )e median waiting time for males was 082times lower than that of females As for the CGPA earnedfrom the university it was found that compared to theinterval of 374ndash40 CGPA receivers graduates who earnedCGPA in 324ndash375 range have to wait 131 times (p value
009) and 275ndash324 graders have to wait 171 times (p valuelt0001) while low achiever (20ndash274) graduates have towait 232 times (p value lt0001) longer When comparinggraduates who were ordinally from urban areas to thosewho were from rural those who were from rural areas hadto wait 215 times (p value lt0001) longer to find their firstjob revealing that graduates from urban areas had shorterwaiting time to first employment compared to those fromrural areas
)ose graduates from all colleges had longer waitingtimes for first employment as compared to the college ofhealth science and medicine However the difference in thewaiting time of first employment between school of law andcollege of health science and medicine is not statisticallysignificant (TR 071 p value 03) )e results in Table 2also show that the median waiting time until first em-ployment for graduates who studied their preferred fieldswas 08 times (p value 0049) shorter than that of graduateswho did not study their preferred fields
6 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
the first fifteenmonths However about sixteenmonths aftergraduation the unemployment rate of females has decreasedfaster than that of males Consequently the differences
between the two curves become almost nonexistent after 16months after graduation )e unemployment curves of thegraduates are considerably different for each collegefaculty
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
Figure 1 KaplanndashMeier curve for the waiting time until the first employment
p = 00004000
025
050
075
100
Une
mpl
oym
ent r
ate
FemaleMale
Sex
Time since graduation in months0 5 10 15 20
(a)
000
025
050
075
100U
nem
ploy
men
t rat
e
p lt 00001
CGPA2ndash274275ndash324
325ndash374375ndash40
0 5 10 15 20Time since graduation in months
(b)
Time since graduation in months0 5 10 15 20
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
CollegefacultyCaNaRMCBECHMIEBS
LawNCSIOT
(c)
0 5 10 15 20Time since graduation in months
000
025
050
075
100
Une
mpl
oym
ent r
ate
p lt 00001
ResidenceRuralUrban
(d)
Figure 2 KaplanndashMeier curve for the waiting time for the first employment by gender college CGPA region and residence of graduatesCANaRM College of Agriculture and Natural Resource Management CHM College of Health Science and Medicine IOT Institute ofTechnology IEBS Education and Behavioral Science NCS Natural and Computational Sciences College and CBE College of Business andEconomics
Education Research International 5
that the students graduate from It is clear that fromFigure 2(c) that graduates from the health science andmedicine unemployment rate dropped faster than that of thegraduates from the remaining colleges in the study tellinggraduates from Health Science and Medicine found em-ployment much faster than the other graduates from othercollegesfaculty )e employment rate of law school grad-uates stayed constant up to 12 months after their graduationalthough it sharply dropped after 12 months of theirgraduation )is is for the fact that the majority of lawgraduates were on inductive training before they wereassigned for their first job by the government
33 Cox Proportional Hazard Model Result )e first stepconsidered in the model building procedure was to explorethe relationship between each covariate and time to em-ployment univariately Accordingly in the univariate Coxproportional hazards regression analysis age at graduation (pvalue lt0001) gender (p value lt0001) collegeinstituteschool categorization of the graduates (p value lt0001) gradepoint average (p value lt0001) the region where the graduatewere from (p value002) place of residence (p value lt0001)and field of study preference (p value 002) show a statis-tically significant association with time to first employment atthe 5 level of significance However parentrsquos educationlevels (p value 02 each) ever receiving consultancy serviceabout job hunting (p value 03245) and study area prefer-ence were found to have no significant association )emultivariable model containing all the significant covariatesin the univariable analysis is described in Table 2
34 PH Assumption Assessment and Overall Goodness-of-FitIncorporating variable(s) not satisfying the PH assumptionleads to an inferior fit of a Cox model that is the power oftest is reduced for both variables with constant and non-constant HR in the model [33] Table 3 reveals the p values ofthe tests based on the scaled Schoenfeld residuals fornonproportional hazard assessment generated by thecoxzph function survival package in R software )e resultsof the test support evidence of deviation from the pro-portionality assumption)is is because some of the p valuesfor testing whether the correlation between Schoenfeld re-sidual for these covariates and ranked survival time is lessthan 005
As a result accelerated failure time models with differentdistributional assumptions were built to model the waitingtime to first employment
35 Accelerated Failure Time Model Results Parametricmodels such as Weibull log-normal log-logistic and ex-ponential models were carried out to identify a model thatfits the data better )e summary of log-likelihood and AICis presented in Table 4 Akaikersquos information criterion (AIC)statistic for the parametric and semiparametric survivalmodels are 2191555 2194743 2188247 and 2214241 forWeibull log-normal log-logistic and exponential models
respectively )e rule is that any model that conforms to theobserved data should adequately lead to a smaller AICHence the log-logistic model appears to be with minimumAIC and BIC values among all other competing parametricmodels revealing that it is the most efficient model toidentify the predictors of the waiting time to first employ-ment of the new graduates
)e result for log-logistic which is a relatively efficientmodel is presented in Table 2 with the estimated values ofthe coefficients time ratio (TR) and its 95 CI and p valueAlthough the proportional hazard assumption was violatedthe results of the Cox PHmodel are also presented alongsidefor comparison purpose )e result of the log-logistic modelis similar to that of the hazard models in detecting thesignificant predictors of time to first employment and theirdirectional effects (positive or negative effect) However theinterpretations are not the same Nevertheless gender andfield of study preference had a statistically significant as-sociation with the waiting time for the first employmentbased on the log-logistic model at 5 level of significance butnot in the Cox PH model
)e estimate of shape parameter in the log-logistic withgamma was 063 which is less than unity suggesting thatthe probability of getting a job decreases monotonicallywith time After adjusting for other independent variablesage at graduation gender collegefaculty CGPA and placeof residence were associated with waiting time to firstemployment A predictor with a positive coefficient (timeratio or acceleration factor greater than unity) implies thatthe variables prolong the waiting time to first employmentAccordingly the acceleration factor for age was 086 (pvalue lt0001) indicating that older graduates had thetendency to have shorter waiting times until first em-ployment )e median waiting time for males was 082times lower than that of females As for the CGPA earnedfrom the university it was found that compared to theinterval of 374ndash40 CGPA receivers graduates who earnedCGPA in 324ndash375 range have to wait 131 times (p value
009) and 275ndash324 graders have to wait 171 times (p valuelt0001) while low achiever (20ndash274) graduates have towait 232 times (p value lt0001) longer When comparinggraduates who were ordinally from urban areas to thosewho were from rural those who were from rural areas hadto wait 215 times (p value lt0001) longer to find their firstjob revealing that graduates from urban areas had shorterwaiting time to first employment compared to those fromrural areas
)ose graduates from all colleges had longer waitingtimes for first employment as compared to the college ofhealth science and medicine However the difference in thewaiting time of first employment between school of law andcollege of health science and medicine is not statisticallysignificant (TR 071 p value 03) )e results in Table 2also show that the median waiting time until first em-ployment for graduates who studied their preferred fieldswas 08 times (p value 0049) shorter than that of graduateswho did not study their preferred fields
6 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
that the students graduate from It is clear that fromFigure 2(c) that graduates from the health science andmedicine unemployment rate dropped faster than that of thegraduates from the remaining colleges in the study tellinggraduates from Health Science and Medicine found em-ployment much faster than the other graduates from othercollegesfaculty )e employment rate of law school grad-uates stayed constant up to 12 months after their graduationalthough it sharply dropped after 12 months of theirgraduation )is is for the fact that the majority of lawgraduates were on inductive training before they wereassigned for their first job by the government
33 Cox Proportional Hazard Model Result )e first stepconsidered in the model building procedure was to explorethe relationship between each covariate and time to em-ployment univariately Accordingly in the univariate Coxproportional hazards regression analysis age at graduation (pvalue lt0001) gender (p value lt0001) collegeinstituteschool categorization of the graduates (p value lt0001) gradepoint average (p value lt0001) the region where the graduatewere from (p value002) place of residence (p value lt0001)and field of study preference (p value 002) show a statis-tically significant association with time to first employment atthe 5 level of significance However parentrsquos educationlevels (p value 02 each) ever receiving consultancy serviceabout job hunting (p value 03245) and study area prefer-ence were found to have no significant association )emultivariable model containing all the significant covariatesin the univariable analysis is described in Table 2
34 PH Assumption Assessment and Overall Goodness-of-FitIncorporating variable(s) not satisfying the PH assumptionleads to an inferior fit of a Cox model that is the power oftest is reduced for both variables with constant and non-constant HR in the model [33] Table 3 reveals the p values ofthe tests based on the scaled Schoenfeld residuals fornonproportional hazard assessment generated by thecoxzph function survival package in R software )e resultsof the test support evidence of deviation from the pro-portionality assumption)is is because some of the p valuesfor testing whether the correlation between Schoenfeld re-sidual for these covariates and ranked survival time is lessthan 005
As a result accelerated failure time models with differentdistributional assumptions were built to model the waitingtime to first employment
35 Accelerated Failure Time Model Results Parametricmodels such as Weibull log-normal log-logistic and ex-ponential models were carried out to identify a model thatfits the data better )e summary of log-likelihood and AICis presented in Table 4 Akaikersquos information criterion (AIC)statistic for the parametric and semiparametric survivalmodels are 2191555 2194743 2188247 and 2214241 forWeibull log-normal log-logistic and exponential models
respectively )e rule is that any model that conforms to theobserved data should adequately lead to a smaller AICHence the log-logistic model appears to be with minimumAIC and BIC values among all other competing parametricmodels revealing that it is the most efficient model toidentify the predictors of the waiting time to first employ-ment of the new graduates
)e result for log-logistic which is a relatively efficientmodel is presented in Table 2 with the estimated values ofthe coefficients time ratio (TR) and its 95 CI and p valueAlthough the proportional hazard assumption was violatedthe results of the Cox PHmodel are also presented alongsidefor comparison purpose )e result of the log-logistic modelis similar to that of the hazard models in detecting thesignificant predictors of time to first employment and theirdirectional effects (positive or negative effect) However theinterpretations are not the same Nevertheless gender andfield of study preference had a statistically significant as-sociation with the waiting time for the first employmentbased on the log-logistic model at 5 level of significance butnot in the Cox PH model
)e estimate of shape parameter in the log-logistic withgamma was 063 which is less than unity suggesting thatthe probability of getting a job decreases monotonicallywith time After adjusting for other independent variablesage at graduation gender collegefaculty CGPA and placeof residence were associated with waiting time to firstemployment A predictor with a positive coefficient (timeratio or acceleration factor greater than unity) implies thatthe variables prolong the waiting time to first employmentAccordingly the acceleration factor for age was 086 (pvalue lt0001) indicating that older graduates had thetendency to have shorter waiting times until first em-ployment )e median waiting time for males was 082times lower than that of females As for the CGPA earnedfrom the university it was found that compared to theinterval of 374ndash40 CGPA receivers graduates who earnedCGPA in 324ndash375 range have to wait 131 times (p value
009) and 275ndash324 graders have to wait 171 times (p valuelt0001) while low achiever (20ndash274) graduates have towait 232 times (p value lt0001) longer When comparinggraduates who were ordinally from urban areas to thosewho were from rural those who were from rural areas hadto wait 215 times (p value lt0001) longer to find their firstjob revealing that graduates from urban areas had shorterwaiting time to first employment compared to those fromrural areas
)ose graduates from all colleges had longer waitingtimes for first employment as compared to the college ofhealth science and medicine However the difference in thewaiting time of first employment between school of law andcollege of health science and medicine is not statisticallysignificant (TR 071 p value 03) )e results in Table 2also show that the median waiting time until first em-ployment for graduates who studied their preferred fieldswas 08 times (p value 0049) shorter than that of graduateswho did not study their preferred fields
6 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
4 Discussion
Despite all the advantages of the Cox model [22] in terms ofmodeling time-to-event data such as waiting time to firstemployment it has drawbacks when the proportional hazardassumption is violated When the assumption of propor-tional hazard was violated fully parametric AFTmodels can
be used as an alternative to model time-to-event data such astime to first employment In this study the acceleratedfailure time (AFT) model was employed to analyze time tofirst employment data Among the parametric AFTmodelsthe log-logistic parametric model fitted the data well )emedian time to first employment of the graduate was 15months which is a longer time compared to the study
Table 2 Analysis of associated factors of unemployment time based on Cox PH and log-logistical AFT models
Table 3 Proportional hazard assumption checking for the covariates
Covariates Chi-square value Df p value Does PH assumption holdAge 9784 1 0002 NoGender 0399 1 053 YesCollegefaculty 86321 7 lt0001 NoRegion 5727 5 033 YesCGPA 1478 3 069 YesResidence 1321 1 025 YesStudying the preferred fields of study 0372 1 054 YesGLOBAL 94451 19 lt0001 No
Table 4 Summary of AIC and BIC values for different survival models
Model Log-likelihood for the null model Log-likelihood for the current model Df AIC valueWeibull minus123686 minus107978 16 2191555Log-normal minus123162 minus108137 16 2194743Log-logistic minus123159 minus107812 16 2188247EXP minus123798 minus109212 15 2214241CPHM minus338004 minus324589 14 6519771
Education Research International 7
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
conducted in Sri Lanka where nearly 50 of the graduatesgot their first job by 12 months after their graduation [34])is variation would have happened due to the differences inthe study areas and years of graduation
)e study revealed that males had shorter unemploy-ment spells than that of females )is finding is similar to theprevious studies conducted in Tanzania [35] but it con-tradicted a study conducted in Ethiopian by Kong and Jiangand in China [36 37] which showed that female graduatesare more likely to enter the labor market ahead of males)isis possibly attributed to the difference in study time andplace )e result also revealed that graduates who were in ahigher CGPA category had shorter unemployment spells)is result is in line with the tracer study results of Bahir DarUniversity graduates Ethiopia [38] and a study conductedin China [14] One possible reason could be in Ethiopia thenumber of job applicants is usually much higher than thenumber of vacancies where employers use academic grade(CGPA) as an elimination criterion thereby graduates witha better achievement have more chance of being recruited aspossible candidates Moreover employers of graduates thinkthat graduates with a better academic performance usuallymeasured by cumulative grade point average as hard-working and smart candidates who can perform better attheir company In result it was also revealed that graduateswho studied their preferred fields had shorter waiting time tofirst employment compared to those compared to graduateswho did not study their preferred fields )is is in line with astudy performed in Ethiopia by Cox [22])is is the fact thatstudents who studied usually have enough motivation tostudy thereby achieving better whereas lack of interest inthe field of study can lead to academic failure In the study itwas revealed that the probability of getting a job decreasesmonotonically with time )is result is in line with a studyconducted in Croatia [39] )is is the fact that employersmay think that long-term unemployed face loss of skills andthe substantial expenditures that are necessary to restorethese skills [40]
5 Conclusion
)is study is based on a dataset on the waiting time to firstemployment derived fromDMU 2018 graduate tracer surveydata to examine the comparative performances of Cox andparametric models for the analysis of time to first em-ployment Although parametric models assume a specificdistribution for the event (waiting time to first employment)they can be used as an alternative model for the Cox modelwhen the proportional hazard assumption fails In thisparticular study the log-logistic parametric model yieldedthe smallest possible AIC and could be taken as the bestfitted model for the data well as compared to other para-metric models Based on the log-logistic model graduatesrsquoaverage time span of unemployment was significantly af-fected by the graduatesrsquo gender age collegefaculty cu-mulative grade point average (CGPA) place of residenceregion where the graduates were from and achievement(measured by CGPA) Crudely only 50 of the graduates
managed to find their first job by 15 months after theirgraduation date which is far less than the universityrsquos targetwhere about 69 of its graduates could secure their first jobby 12 months after graduation
6 Recommendation and Policy Implications
)e estimated 12 months employment rate (44) is farbelow the universityrsquos target (69) Hence for effectivetransition of graduates to the labor market the universityshould have a fully functioning career service office which isstaffed with ample professionals and optimal resources toprovide training on job hunting to deliver the soft skillseffectively and to arrange job fair programmers tostrengthen relationships with employers )e universitytogether with its stakeholders should encourage the provi-sion of entrepreneurship educational practices and trainingsto cultivate an entrepreneurial mindset among graduatesand turn them into job creators instead of job seekersMoreover Ethiopian Ministry of Science and Higher Edu-cation should work with ministry of labor affair and otherstokeholds to align the education programs in line with thedemand of the labor market
Abbreviations
KM KaplanndashMeierDMU Debre Markos UniversityCGPA Cumulative grade point averageAIC Akaike information criterionAFT Accelerated failure timePH Proportional hazard
Data Availability
)e datasets used to support this study are available from thecorresponding author upon reasonable request
Ethical Approval
)e researchers have got permission from the office of thedelivery unit Debre Markos University to use graduatedtracer survey data without fabrication and falsification ofdata
Conflicts of Interest
)e authors declare that they have no conflicts of interest
Authorsrsquo Contributions
MGA contributed to the study concept and design of thestatistical methodology performed the analysis interpretedthe data and wrote the first draft of the manuscript AAcontributed to the study on critical revision of the manu-script and AW assisted in analyzing the study and wrote upthe manuscript All the authors read and approved the finalmanuscript
8 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
Acknowledgments
)e authors are grateful to DebreMarkos University office ofdelivery unit for the permission to use the data )is workwas financially supported by Debre Markos University
Supplementary Materials
R codes used for the analysis of the waiting time to firstemployment of new graduates using the survival model(PDF 288 kb) are given (Supplementary Materials)
References
[1] NW Reda andM T Gebre-Eyesus ldquoGraduate unemploymentin Ethiopia the lsquored flagrsquoand its implicationsrdquo InternationalJournal of African Higher Education vol 5 no 1 2018
[2] J Yibeltal Higher Education and Labor Market in Ethiopia ATracer Study of Graduate Employment in Engineering fromAddis Ababa and Bahir Dar Universities Addis Ababa Uni-versity Addis Ababa Ethiopia 2016
[3] D Gebretsadik -e Cause of Educated Youth Unemploymentand Its Socioeconomic Effect in Addis Ababa Addis AbabaUniversity Addis Ababa Ethiopia 2016
[4] G A Akalu ldquoHigher education lsquomassificationrsquo and challengesto the professoriate do academicsrsquo conceptions of qualitymatterrdquo Quality in Higher Education vol 22 no 3pp 260ndash276 2016
[5] A Tessema and M Abebe ldquoHigher education in Ethiopiachallenges and the way forwardrdquo International Journal ofEducation Economics and Development vol 2 no 3pp 225ndash244 2011
[6] M M Batu ldquoDeterminants of youth unemployment in urbanareas of Ethiopiardquo International Journal of Scientific andResearch Publications vol 6 no 5 2016
[7] R Shakir ldquoSoft skills at the Malaysian institutes of higherlearningrdquo Asia Pacific Education Review vol 10 no 3pp 309ndash315 2009
[8] M Groh N Krishnan D McKenzie and T VishwanathldquoSoft skills or hard cashrdquo in-e Impact of Training and WageSubsidy Programs on Female Youth Employment in Jordan)e World Bank Washington DC USA 2012
[9] S Majid Z Liming S Tong and S Raihana ldquoImportance ofsoft skills for education and career successrdquo InternationalJournal for Cross-Disciplinary Subjects in Education vol 2no 2 pp 1037ndash1042 2012
[10] K Sławinska and C S Villani ldquoGaining and strengtheninglsquosoft skillsrsquo for employmentrdquo Edukacja Ustawiczna Dorosłychvol 3 no 86 pp 44ndash53 2014
[11] O S Pitan and S O Adedeji Skills Mismatch among Uni-versity Graduates in the Nigeria US-China Education Reviewvol 2 no 1 pp 90ndash98 2012
[12] E F Arruda D B Guimaratildees I Castelar and P CastelarldquoDeterminants of long-term unemployment in Brazil in2013rdquo International Journal of Economics and Finance vol 10no 6 2018
[13] F Niragire and A Nshimyiryo ldquoDeterminants of increasingduration of first unemployment among first degree holders inRwanda a logistic regression analysisrdquo Journal of Educationand Work vol 30 no 3 pp 235ndash248 2017
[14] K Jun ldquoFactors affecting employment and unemployment forfresh graduates in Chinardquo in Unemployment Perspectives andSolutions p 53 Intech Open London UK 2017
[15] D Jackson ldquoFactors influencing job attainment in recentBachelor graduates evidence from Australiardquo Higher Edu-cation vol 68 no 1 pp 135ndash153 2014
[16] J Dania A R Bakar and S Mohamed ldquoFactors influencingthe acquisition of employability skills by students of selectedtechnical secondary school in Malaysiardquo International Edu-cation Studies vol 7 no 2 pp 117ndash124 2014
[17] M I Hossain A Kalaiselvi P Yagamaran et al ldquoFactorsinfluencing unemployment among fresh graduates a casestudy in Klang Valley Malaysiardquo International Journal ofAcademic Research in Business and Social Sciences vol 8no 9 pp 1494ndash1507 2018
[18] G Mohamedbhai ldquo)e challenge of graduate unemploymentin Africardquo International Higher Education vol 80 no 80p 12 2015
[19] Y Hwang ldquoWhat is the cause of graduatesrsquo unemploymentFocus on individual concerns and perspectivesrdquo Journal ofEducational Issues vol 3 no 2 pp 1ndash10 2017
[20] J Y Yizengaw ldquoSkills gaps and mismatches private sectorexpectations of engineering graduates in Ethiopiardquo IDSBulletin vol 49 no 5 2018
[21] Z Siraye T Abebe M Melese and T Wale ldquoA tracer studyon employability of business and economics graduates atBahir Dar Universityrdquo International Journal of Higher Edu-cation and Sustainability vol 2 no 1 pp 45ndash63 2018
[22] D R Cox ldquoPartial likelihoodrdquo Biometrika vol 62 no 2pp 269ndash276 1975
[23] W G Cochran ldquo)e estimation of sample sizerdquo SamplingTechniques vol 3 pp 72ndash90 1977
[24] J Klein and M Moeschberger Survival Analysis Techniquesfor Censored and Truncated Data Springer New York NYUSA 1997
[25] J Orbe E Ferreira and V Nuntildeez-Anton ldquoComparingproportional hazards and accelerated failure time models forsurvival analysisrdquo Statistics in Medicine vol 21 no 22pp 3493ndash3510 2002
[26] E L Kaplan and P Meier ldquoNonparametric estimation fromincomplete observationsrdquo Journal of the American StatisticalAssociation vol 53 no 282 pp 457ndash481 1958
[27] W LaMorte Cox Proportional Hazards Regression AnalysisBoston University School of Public Health Boston MA USARetrieved September p 2018 2016
[28] D W Hosmer Jr S Lemeshow and S May Applied SurvivalAnalysis Regression Modeling of Time-To-Event Data JohnWiley amp Sons Hoboken NJ USA 2011
[29] M A Pourhoseingholi E Hajizadeh B Moghimi DehkordiA Safaee A Abadi and M Reza Zali ldquoComparing cox re-gression and parametric models for survival of patients withgastric carcinomardquo Asian Pacific Journal of Cancer Preven-tion vol 8 no 3 pp 412ndash416 2007
[30] L A Gelfand D P MacKinnon R J DeRubeis andA N Baraldi ldquoMediation analysis with survival outcomesaccelerated failure time vs proportional hazards modelsrdquoFrontiers in Psychology vol 7 p 423 2016
[31] S P Khanal V Sreenivas and S K Acharya ldquoAcceleratedfailure time models an application in the survival of acuteliver failure patients in Indiardquo International Journal of Scienceand Research (IJSR) vol 3 no 6 pp 161ndash166 2014
[32] H Akaike ldquoFactor analysis and AICrdquo in Selected Papers ofHirotugu Akaike pp 371ndash386 Springer Berlin Germany 1987
[33] O J Achilonu J Fabian and E Musenge ldquoModelling long-term graft survival with time-varying covariate effects anapplication to a single kidney transplant centre in
Education Research International 9
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
10 Education Research International
Johannesburg South Africardquo Frontiers in Public Healthvol 7 p 201 2019
[34] I T Jayamanne and K A Ramanayake ldquoA study on thewaiting time for the first employment of arts graduates in SriLankardquo International Journal of Computer and InformationEngineering vol 11 no 12 pp 1167ndash1175 2017
[35] N E Nikusekela and E M Pallangyo ldquoAnalysis of supply sidefactors influencing employability of fresh higher learninggraduates in Tanzaniardquo Global Journal of HumanndashSocialScience Economics vol 16 no 1 2016
[36] J Kong and F Jiang ldquoFactors affecting employment un-employment and graduate study for university graduates inBeijingrdquo in Proceedings of the International Conference onAdvances in Education and Management Dalian ChinaAugust 2011
[37] J Kong ldquoCollege discipline and sex factors effecting em-ployment opportunities for graduatesrdquo in Proceedings of the2013 International Conference on the Modern Development ofHumanities and Social Science Hong Kong China December2013
[38] H M Fenta Z S Asnakew P K Debele S T Nigatu andA M Muhaba ldquoAnalysis of supply side factors influencingemployability of new graduates a tracer study of Bahir DarUniversity graduatesrdquo Journal of Teaching and Learning forGraduate Employability vol 10 no 2 p 67 2019
[39] P Bejakovic and Z Mrnjavac ldquo)e danger of long-termunemployment and measures for its reduction the case ofCroatiardquo Economic Research-Ekonomska Istrazivanja vol 31no 1 pp 1837ndash1850 2018
[40] G Jarosch and L Pilossoph -e Longer Yoursquore Unemployedthe Less Likely You Are to Find a Job Why World EconomicForum Cologny Switzerland 2016
