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Principal component and factors analysis will be used to summarize each multidimensional
variables (household head characteristics, socio-economics characteristic, biophysical factors,
household income factors, expenditures factors, and multidimensional poverty indicators) this
process give a standardize score or weight for each, which are usually referred to as the
composite variables or latent variables. The process is a statistical technique commonly used to
build a predictive or descriptive model of group discrimination, based on priory existence of
distinct class or group in the variables, the model classify each observation into one of the
group.Sabine,L. and Brian S. E., 2004; Peter T., 1997; Koustsoyiannis, 2001 all claimed that it is
an approach of summarizing and uncovering any patterns in a set of multivariate data, essentially
by reducing the complexity of the data and providing a factor from the unclassified variables
which has a greater power of contribution on the relationship. The technique also served as
means of investigating whether a number of variables of interest are linearly related to a smaller
number of unobservable factors commonly known as the latent factors or composite variables.
( Sabine, L. 2004, Alkire, S and Maria, E., 2010; Foster, J.E. 2007; Joseph, F,. William, C.B.,
Barry, J.B., and Rolph, E.A., 2010). This weighted scores, composite variables or latent variables
are used examine the interrelationship between the variables, setting the rest as independent
while multidimensional poverty factors are set as dependent variable whose effect are
determined by the action of the independent. This process was carried out because
multidimensional poverty relationship is complex and interdependent hence cannot be separatedinto dependent and independent variables straight away( Joseph, F,. William, C.B., Barry, J.B.,
and Rolph, E.A., 2010; Anonymous, 2011; Wilkinson D.J. 2012; Asselin, L.M and Tuan, A.V
2009; Rencher, A.C 2002; Abdeljaouuad, E and Paolo, V 2012; Heikon, C., Justinia, R and
Robert, D, 2011;Neil,H.T 2002, Rodrigo,P 2011 Hardle,W. and Simar L, 2003 ) but with this
analysis the complexity will be broken and hence allow for categorization between a dependent
and independent variables and can be used for further analysis.
3.8 Conceptual framework
Indeed, Poverty has various sign including lack of income and productive resources sufficient to
ensure sustainable livelihood; hunger and malnutrition, ill-health limited or lack of access to
education and other basic services; increased morbidity and mortality from illness; homelessness
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and in adequate housing; unsafe environments; and social discrimination and exclusion which is
characterized by lack of participation in decision making and civil, social and cultural life. The
traditional method of measuring poverty were basically using continuous interval scales on
income or expenditure and set a poverty line, however this method has not been comprehensive
in providing a clear understanding of the poverty.
Perhaps, this set the need to understand the relationship between the actual multidimensional
poverty and the variables used to measure poverty previously (such as Income and expenditure),
however these multidirectional variables require the use of categorical and ordinal variables to
capture and measure all the aspects consider to reflect the poverty. However, these variables are
numerous which need to prune but an objective process of pruning is to be undertaking using
statistical approach to extract the hidden variable of Poverty, Income and expenditure which can
be used for the assessment of relationship. The use of such statistical tool to reduce the response
variables is because of wide inter-correlation within the variable which if allowed will affect the
estimation and basically make the standard error of estimates to be badly biased and hence result
in the breaking down of the assumption of multiple linear regression so by this practice it serves
in solving the problem of multi-collinearity observed within variable and maintaining the
variability of the response. Schematically the description of the variables based on research
objectives is as follows:
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Model for Analysis of Interdependent relationship among multidimensional poverty determinants of Farmers in Gombe North
3.0 METHODOLOGY
3.1 Study Area
The study will be carried out in five local government area of Gombe state (Gombe north
senatorial zone) the survey is to be conducted include Dukku, Funakaye, Gombe, Kwami, and
Nafada. The study area has a land mass of d six hundred and fifty five square kilometres
(8655km2), has a total population figure of six hundred and seventeen thousand eight hundred
and four (617,804)people out of which are four hundred and eighty thousand five hundred and
eighty four (480584; 77.8%) males with two hundred and nine thousand two hundred and twenty
(209220; 22.2%) females. Gombe north was bounded by Darazau (Bauchi state) from the north,
Kumo and Akko village all in Akko L.G.A. (Gombe central) from the south and west
respectively, by Kwadon in Yamaltu-Deba L.G.A. (Gombe central), North east by Ngalda in
Potiskum, LGA (Yobe state). There are twenty eight thousand two hundred (28,200) households
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in the 5 local government areas to be surveyed with an average household size of 11 people,
nearly half of which are females.
Gombe north lies at altitude 700 207m above sea level has a maximum temperature 40.80C
and mean temperature 15.30C with the coldest months between December and February. The
hottest months ranges from March to May with temperature of up to 33.60C, the mean
temperature fall up to 180C with the coldest month from November to February (Baba D. 1999).
Gombe has unimodal rainfall distribution with total annual rainfall of 1528mm and mean annual
rainfall of 109mm with total annual rainy days of a 129 days rain and a mean 9 days per month.
The rainfall spread between the months of April to October the local government is characterized
by savannah grass land some woody trees of height ranging from 2m to 3.5m. The dominants
trees include Khaya (Madaci), neam (dogonyaro), parkia trees(Locust bean). The soil is
predominated by sandy to sandy loam with a pH ranging from 6.0 7.5 low in Nitrogen, with a
C.E.C (cations exchange capacity) ranging between 21 35%. The major crops grown are maize,
millet, cowpea, cotton, groundnut, bambara nut and cassava, vegetables include onion, tomato,
pepper.
Rice production in the zone is not widespread. This is because of the rainfall situation and
absence of water reservoirs, only Nafada, Hashidu had the potential for rice production because
of the existence of river Gombe Abba and Hashidu(Hassan, M. 2011)
3.2 Sampling procedure and Sample Size
Multistage sampling method will be employed to sample three hundred farming households. At
the first stage, all local government in the study area will be selected, they include: Dukku,
Funakaye, Gombe, Kwami and Nafada. The second stage involves the random selection of threefarming communities (villages) from each local government area. The third stage sampling
involves proportionate random sampling selection of twenty farming household from each
community (village). A total of three hundred farming households will constitute the sample size
for the study. The sampling plan is presented in table 1.
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3.3 Sample frame
Table 1: The sampling plan for the study
LGA Community
Distance
from LGA
Distance from
State(Km)
Estimated Male
Population
Estimated Female
Population
Total
Population
Number of
Household
Dukku
Dukku 0 73 18879 9782 28661 2697
Gombe Abba 19.12 85.39 2934 1487 4421 267
Hashidu 29.9 87.65 3313 1716 5029 331
Jarkum 14.51 64.25 3541 1716 5257 393
Malala 44.54 92.45 11223 5550 16773 1603
Zange 28.74 51.33 1397 808 2205 93
Funakaye
Ashaka Gari 9.45 78.01 4622 2339 6961 385
Bage 12.34 78.93 2051 1063 3114 205
Bajoga 0 71.12 35964 18738 54702 2398
Ribadu 32.4 45.44 1710 864 2574 132
Wawa 34.28 57.54 5231 25247755 265
WuroBapparu 14.58 76.37 751 362 1113 50
Gombe
Bajoga 0 3.5 NA NA NA NA
Shamaki 2.6 2.6 55942 29551 85493 3729
Dawaki 2.36 2.36 20343 10746 31089 1356
Bolari 2.16 2.16 50854 26863 77717 3390
Fantami 1.5 1.5 30514 16119 46633 2034
Jekadafari 1.9 1.9 35600 18805 54405 1978
London
Maidoruwa 3.2 3.2 20343 10746 31089 1565
Kumbiya-
Kumbiya 3.5 1.5 NA NA NA NA
Ajiya 3.5 1.5 25428 13432 38860 1496
Kwami
Kwami 49.5 13.53 7112 2401 9513 790
Malam Sidi 0 25.92 4226 2255 6481 352
Bojude 58.7 32.65 8819 2868 11687 802
Tappi 53 26.68 4843 1696 6539 484
Doho 7.9 19.14 3339 1629 4968 304
Dukul 22 43.84 4906 2439 7345 491
Nafada
BarwoWunde 8.14 91.65 2798 1424 4222 233
Nafada 0 97.88 13512 6784 20296 901
Jigawa 33.56 126.36 3966 1829 5795 406
BarwoNasarawa 10.44 92.11 12038 6501 18539 926
Birin Bolawa 25.03 70.52 6290 3154 9444 419
Birin Fulani 24.87 71.48 6095 3029 9124 406
Total 480584 209220 617804 30881
Source: Hassan M (2011)
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3.7 Method of Data Collection
The study will obtain data majorly from primary source. Structured questionnaire will be used as
an instrument for data collection on household level. The questions will feature socioeconomics
and demographic information of the households, household head characteristics, poverty pointers
and associated features, households perceptions on the causes of poverty; households
information on income, expenditure and some biophysical features of farmers farms.
3.9 Analytical Technique and Model Specification
Combinations of analytical techniques will be employed for data analysis to achieve the
objectives of this study. These will include descriptive which include mean, mode median as
well as inferential statistics using multivariate technique which include cluster analysis, principal
component analysis, multidimensional scaling, stepwise regression, discriminant, factor analysis,
conjoint analysis and correspondence analysis.
3.4.1 Descriptive and Inferential Statistics
Descriptive statistics such as mean, standard deviation, frequency distribution will be used to
describe the data and is used to achieve objective 1, while
responses on the socio economics and demographic characteristics, households perceptions on
the causes of land degradation;land use pattern and management. This will be used to achieve
objective 1, 2 and 8 as well as part of objectives 4 and 6. Cross tabulation will be use to
disaggregate the variable by household land use type, State and community type.
Inferential statistics in the form of Chi-square and t test will be used to test the statistical
significance of the relationships or differences between variables as well as the goodness of fit of
the distribution. More specifically, Chi-square test will be used to test hypotheses 1 and 2.
Stepwise regression will be done on the collected data. The first step will use principal
component analysis, factor analysis and discriminant to trim the number of variables (The one
that fitted most will be taken).
3.9.2 Measurement of Composite (Latent) variables
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It is common practice in socioeconomics studies to compute latent or composite variables on
parameters like socio-economic factors, quality assurance, these parameters are usually gotten
from several observed indicators (response items) each requiring responses in dichotonomous,
polychotonomous (likert type), ordered categories. Traditionally product moment correlation is
used in such composite scores or weighted variables, through their additive indices of these
indicators without regard to either measurement and distributional properties of the constituents
indicators or their relative contribution to the composite score. While, the Composite score so far
gotten are then treated as continuous variables in compilation in general linear model technique,
which assume that such variables are measured without error.
Consequently, this approach leads to at least two major problems when trying to model
relationship among composite scores or when comparing, their magnitude and weighed additives
are ignored, in that some indicators contribute more to measurement of the composite than others
the second it may invalidates the composite score if one or more of the indicators measure a
construct other than the one under consideration. Hence this new insight is helpful in minimizing
the problem so far encountered in the traditional method.(Ken, R. 2006), Karl, G.J. and Irini, M.
(2001)
The basic idea behind the analysis is that, given a set of ordinal or categorical response variable
X1,X2.Xp, after the analysis a latent factor z1,z2..zk fewer in number than the observed
variable are obtained but contain essentially the same information which is called a latent factor.
These latent factors are to account for the dependencies among the response variables, in the
sense that if the factor is held fixed the observed variable would be independent. The latent
function involves the determination of linear equation like regression that will predict which
group the case belongs to.
Latent function can express as below;
LFj= Li1X1 + Li2X2++LipXp + a
Where the LFj = Latent factor function, Li=Latent co-efficient or weight for that variable, X=
respondents score for that variable a= constant, i=number of predictor variables. The function is
similar to regression but its co-efficient are un-standardize co-efficient analogous to the co-
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efficient in regression. These co-efficient maximized the distance between the criterion
(dependent) variable. Standardize latent co-efficient can also be used like beta in weighted
regression. The variable shown below are all inserted into the analytical technique and analysed
the co-efficient obtained from the analysis are latent factors grouped into the categories shown
and were used for further analysis as dependent and independent variables for the second
regression for the assessment of relationship and produce a standardized co-efficient.
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Variables Definition
Latent (composite) variables
Poverty
=Y
Socio Economics
= a1
Household Head Characteristics
= a2
Household Expenditure
= a3
Household Inco
= a4Original variables obtained from survey to be transformed to latent variables
ccessibility &
aterial Lack
xclusion
ulnerability
hysical weakness
ender equality
nvironmental con.
ousing and
othing
=X1
=X2
=X3
=X4
=X5
=X6
=X7
Gender
Age
Marital Status
Family type
Occupation
Religion
Farming Experience
Farm size
Membership of
Co-operative
Category
= X8
= X9
= X10
= X11
= X12
= X13
= X14
=X15
=X16
=X17
Household Size
Number of Children below
18
Number of Others above 18
-60
Number of Elderly above 65
Number of Internal
Migration
Location
Number of years in Co-
operative
Education Level
= X18
= X19
=X20
= X21
= X22
= X23
=X24
=X25
=X26
=X27
Total food expenses =X28 Quantity of
Farm OutputPurchase of Tools
and Animals
=X29
Housing expenses =X30 Total nonfarm
received
Education expenses =X31 Off-farm
receivedTransportation/Co
mmunication
=X32
Repairs and
maintenance
=X33 Total value of
Farm assets
Social contribution =X34 Equipment
Mechanical
Total expenses on
farm
=X36 Tools non
mechanical
EquipmentLoans repayments =X37
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If the factors are independent, it follows that the correlation between and is
From the above equation 1 is a suitable representation of the latent factors in the model if
response variable are continuous variables measured on an interval or ratio scale. However, it
cannot be used if the response variables are ordinal or nominal. In those cases, it is obvious
that the probability of each response pattern as a function of
Hence it becomes
expressed
as
...(4a)
Or
..(4b)
Where responses
ectors of
measurement errors
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Ken, R.(2006) ; Karl,G.J(2001)
3.10 Linear regression model
This model will be used to achieve objective ii of this study. The model is based on the multiple
linear regressions. The function is therefore expressed as:
.. (4)
Where:
= + Xi
= Poverty Score
= Socioeconomics factors, Household expenditure, Household Income, Household
Head characteristics,
= constant term
= regression coefficient
= disturbance term or error term
3.11 Farm budgeting technique:
Household budget as the detailed physical and financial expenses between certain period. Net
household income (NHI) as the difference between the Gross Income (GI) and total expenses
(TE) Total expenditures food + Total non-food expenditure + social expenses + tax
&depreciation (N). (Olukosi and Erhabor, 2005) this technique will be used to compute for total
expenses and is presented with the following equation:
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Net Household Income = GI THE TSE
THE + TSE = TE
Therefore NHI = GI THE - TSE
Where:
NHI = Net Household Income (N)
GI = Gross Income(Farm + Non farm) (N)
THE=Total household expenditure (N)
TSE = Total social expenditure (N)
TE = Total expenditures food+ Total non-food expenditure + social expenses + tax
&depreciation (N)
3.12 Descriptive Statistics
Descriptive statistics will also be used in this study. It involves the use of frequency, percentages,
etc
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