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Sonia M. Bartolomei-Suárez Associate Dean of Academic Affairs, School of Engineering
David González-Barreto Professor, Industrial Engineering Department
Antonio González-QuevedoProfessor, Civil Engineering and Surveying Department
University of Puerto Rico, Mayagüez04/18/23
Using an Expected Loss Function to Identify Best High Schools for
Recruitment
Outline• Introduction• Objectives• Description of Admission Criteria• Performance of our engineering students in their high
schools• Performance of the students at UPRM’s College of
Engineering• Definition of the Performance Index Using Quadratic Loss
Function• Conclusions• Future Work• References• Acknowledgement
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Introduction– A study of our entering student profile demonstrates that a large
number of them come from the Western part of the island of Puerto Rico, our geographic region [1].
– The school of engineering is interested in attracting good students from all the geographic areas of Puerto Rico.
– With this goal in mind, this study was developed to identify the best schools in the island, based on the performance of the engineering students in our university.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Objectives– An objective of the strategic plan of the University of
Puerto Rico Mayagüez (UPRM) is to identify and attract the best possible prospective students from high schools to the College of Engineering.
– To address this objective a good first step is to identify the high schools that produce, over a period of years, the students that better executed within our institution.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Description of Admission Criteria– The admission index, which is called the IGS, is composed of the
high school grade point average, the verbal aptitude, and the mathematics aptitude tests scores from the College Board Entrance Examination.
– The highest possible value of the IGS is 400. – The weight of the GPA is 50%, while the weight for each of the
two aptitude tests is 25% each. – Each academic program determines each year the minimum value
of the IGS. – In general terms, no other measurement is used to admit a
student in the first year of university studies. For the engineer class of 2004-2005, the minimum IGS fluctuated from to 313 for Surveying to 342 for Computer Engineering.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Performance of our engineering students in their high schools
– First this study presents the best high schools, private and public, from the perspective of the student performance in their high schools.
– The high schools that were included in the study have sent more than 50 students who have graduated from our School of Engineering in the past ten years (1995-2005).
– This study was generated using data obtained from the Office of Institutional Research and Planning of our university.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Performance of our engineering students in their high schools
The high schools were analyzed based type of school (private or public) and:
– The number of graduates that entered at the UPRM’s College of Engineering during the years 1995-2005 (the top fifteen).
– The average admission index (IGS) for the graduates that entered at the UPRM’s College of Engineering during the years 1995-2005 (the top fifteen).
Using an Expected Loss Function to Identify Best High Schools for Recruitment
106
106
108
109
112
112
126
127
140
143
146
149
156
182
397
0 50 100 150 200 250 300 350 400 450
Ramón José Dávila, Coamo
Domingo Aponte Collazo, Lares
Secundaria UPR, Río Piedras
Dr. Carlos González, Aguada
Luis Muñoz Marin, Añasco
Benito Cerezo, Aguadilla
Lola Rodríguez de Tió, San Germán
Miguel Meléndez Muñoz, Cayey
Luis Muñoz Marin, Yauco
Blanca Malaret, Sabana Grande
University Gardens, Río Piedras
Efrain Sánchez Hidalgo, Moca
Eugenio María de Hostos, Mayagüez
Patria Latorre, San Sebastian
CROEM, Mayagüez
Esc
uela
s Púb
licas
Cantidad de Estudiantes
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 1. First 15 Public High Schools with 50 or more graduates at UPRM for the College of Engineering (Years 1995-2005).
77
82
86
87
88
88
90
90
96
117
121
122
145
182
262
0 50 100 150 200 250 300
Carvin School, Carolina
Colegio Evagélico Capitán Correa, Arecibo
Colegio San Carlos, Aguadilla
Colegio María Auxiliadora, Carolina
Colegio San Antonio Abad, Humacao
Academia Santa María, Ponce
Colegio San Agustín, Cabo Rojo
American Military, Guaynabo
Colegio Marista, Guaynabo
Colegio San Antonio, Río Piedras
Academia Discípulos de Cristo, Bayamón
Colegio San Ignacio, Río Piedras
Colegio San José, Río Piedras
Academia de la Inmaculada Concepción, Mayagüez
Notre Dame High School, Caguas
Esc
uela
s
Cantidad de Estudiantes
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 2. First 15 Private High Schools with 50 or more graduates at UPRM for the College of Engineering (Years 1995-2005).
336
336
336
337
337
337
337
337
338
339
339
340
340
340
341
341
333 334 335 336 337 338 339 340 341 342
Juan Antonio Corretjer, Ciales
Asunción Rodríguez, Guayanilla
Ponce High School, Ponce
Juan Quirindongo Morell, Vega Baja
Domingo Aponte Collazo, Lares
Patria Latorre, San Sebastían
Luis Muñoz Marin, Añasco
Eladio Tirado López, Aguada
Carmen Bozello de Huyke, Arroyo
Carmen Belén Veiga, Juana Díaz
University Gardens, Río Piedras
Emilio R. Delgado, Corozal
Leonídes Morales Rodríguez, Lajas
Ramón José Dávila, Coamo
Secundaria UPR, Río Piedras
Vocacional Antonio Lucchetti, Arecibo
Esc
uela
s Púb
licas
IGS
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 3. Public High Schools with the highest IGS for graduates of the School of Engineering within 1995-2005.
338
339
339
339
339
339
340
340
340
340
340
340
342
343
343
335 336 337 338 339 340 341 342 343 344
Colegio San Conrado, Ponce
Colegio San Antonio Abad, Humacao
Colegio Evagélico Capitán Correa, Arecibo
Colegio San José, Caguas
Academia Santa María, Ponce
Carvin School, Carolina
Colegio Marista, Guaynabo
Cupeyville School, Río Piedras
Academia de la Inmaculada Concepción, Mayagüez
Colegio Santo Tomás de Aquino, Bayamón
Colegio San José, Río Piedras
Notre Dame High School, Caguas
Colegio San Antonio, Río Piedras
Academia San José, Guaynabo
Colegio Ponceño
Esc
uela
s
IGS
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 4. Private High Schools with the highest IGS for graduates of the School of Engineering within 1995-2005.
Performance of the students at UPRM’s College of Engineering
• After identifying the high schools based on the performance of their students at the high school level, it was decided to analyze the high schools based on the performance of their students at the College of Engineering.
• The high schools were analyzed based on:- the time to complete a BS in engineering - the UPRM graduation grade point average (GPA) - the UPRM graduation rate
Using an Expected Loss Function to Identify Best High Schools for Recruitment
6.12
6.09
6.04
6.03
6.00
6.00
5.97
5.97
5.97
5.87
5.83
5.79
5.79
5.65
5.59
5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.20
SAN GERMAN-LOLA RODZ DE TIO
YAUCO-LUIS MUNOZ MARIN
RIO PIEDRAS-UNIVERSITY GARDENS
AIBONITO-DR JOSE N. GANDARA
LARES-DOMINGO APONTE COLLAZO
AGUADILLA-BENITO CEREZO
JUANA DIAZ-CARMEN BELEN VEIGA
CAYEY-MIGUEL MELENDEZ MUNOZ
OROCOVIS-JOSE ROJAS CORTES
ARROYO-CARMEN BOZELLO DE HUYKE
HUMACAO-ANA ROQUE
SAN SEBASTIAN-PATRIA LATORRE
COAMO-RAMON JOSE DAVILA
CIDRA-ACADEMICA ANA J CANDELAS
RIO PIEDRAS-SECUNDARIA UPR
Escu
ela
s P
úb
licas
Tiempo Promedio
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 5. Top 15 public high schools with the lowest average time to complete the bachelor’s degree in engineering (1991-2006).
5.90
5.88
5.87
5.80
5.78
5.76
5.75
5.70
5.67
5.66
5.66
5.62
5.55
5.52
5.48
5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00
PONCE-ACAD SANTA MARIA
CAROLINA-CARVIN SCHOOL
RIO PIEDRAS-COL SAN JOSE
GUAYNABO-COL SAGRADOS CORAZONES
MAYAGUEZ-ACAD LA INMACULADA
CAGUAS-NOTRE DAME HIGH SCHOOL
RIO PIEDRAS-COL SAN IGNACIO
SAN GERMAN-COL SAN JOSE
AGUADILLA-COL SAN CARLOS
RIO PIEDRAS-COL SAN ANTONIO
CAGUAS-COL SAN JOSE
PONCE-COL PONCENO
RIO PIEDRAS-COL ESPIRITU SANTO
PONCE-COL SAN CONRADO
HUMACAO-COL SAN ANTONIO ABAD
Escu
ela
s P
rivad
as
Tiempo Promedio
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 6. Top 15 private high schools with the lowest average time to complete the bachelor’s degree in engineering (1991-2006).
3.00
3.01
3.01
3.02
3.03
3.04
3.04
3.04
3.04
3.05
3.05
3.06
3.07
3.13
3.22
2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25
ARROYO-CARMEN BOZELLO DE HUYKE
AIBONITO-DR JOSE N. GANDARA
SABANA GRANDE-BLANCA MALARET
CAYEY-MIGUEL MELENDEZ MUNOZ
MAYAGUEZ-CROEM
ANASCO-LUIS MUNOZ MARIN
RIO PIEDRAS-UNIVERSITY GARDENS
AGUADILLA-BENITO CEREZO
HUMACAO-ANA ROQUE
MAYAGUEZ-JOSE DE DIEGO
SAN SEBASTIAN-PATRIA LATORRE
COAMO-RAMON JOSE DAVILA
LARES-DOMINGO APONTE COLLAZO
SAN GERMAN-LOLA RODZ DE TIO
RIO PIEDRAS-SECUNDARIA UPR
Escu
ela
s P
úb
licas
GPA Promedio
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 7. Top fifteen public schools with highest UPRM Graduation Grade Point Average (GPA)for students from public high schools who entered the Faculty of Engineering (1991-2006).
3.04
3.04
3.04
3.04
3.05
3.06
3.07
3.08
3.09
3.12
3.15
3.19
3.20
3.21
3.21
3.22
3.23
2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25
CAROLINA-COL MARIA AUXILIADORA
GUAYNABO-AMERICAN MILITARY
PONCE-COL PONCENO
CABO ROJO-COL SAN AGUSTIN
ISABELA-COL SAN ANTONIO
PONCE-ACAD SANTA MARIA
CAROLINA-CARVIN SCHOOL
CAGUAS-NOTRE DAME HIGH SCHOOL
GUAYNABO-COL SAGRADOS CORAZONES
CAGUAS-COL SAN JOSE
SAN GERMAN-COL SAN JOSE
RIO PIEDRAS-COL SAN ANTONIO
HUMACAO-COL SAN ANTONIO ABAD
PONCE-COL SAN CONRADO
MAYAGUEZ-ACAD LA INMACULADA
AGUADILLA-COL SAN CARLOS
RIO PIEDRAS-COL ESPIRITU SANTO
Escu
ela
s P
rivad
as
GPA Promedio
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 8. Top seventeen private schools with highest UPRM Graduation Grade Point Average (GPA)for students from private high schools who entered the Faculty of Engineering (1991-2006).
64.91
65.00
68.33
68.63
68.97
70.00
70.59
71.67
72.09
72.73
73.21
76.06
80.00
82.46
83.56
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00
LARES-DOMINGO APONTE COLLAZO
SABANA GRANDE-BLANCA MALARET
SAN GERMAN-LOLA RODZ DE TIO
CIDRA-ACADEMICA ANA J CANDELAS
OROCOVIS-JOSE ROJAS CORTES
HUMACAO-ANA ROQUE
MAYAGUEZ-CROEM
RIO PIEDRAS-UNIVERSITY GARDENS
MAYAGUEZ-EUGENIO M DE HOSTOS
COAMO-RAMON JOSE DAVILA
AGUADILLA-BENITO CEREZO
YAUCO-LUIS MUNOZ MARIN
MOCA-EFRAIN SANCHEZ HIDALGO
RIO PIEDRAS-SECUNDARIA UPR
SAN SEBASTIAN-PATRIA LATORRE
Es
cu
ela
s P
úb
lic
as
Tasa de Graduación
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 9. Top fifteen public high schools with the highest UPRM graduation rates for students who entered the School of Engineering in the cohorts of 1991-1997.
58.70
66.67
68.29
73.58
75.56
76.26
78.05
78.05
80.33
81.16
82.22
82.50
90.18
93.02
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
CAROLINA-COL MARIA AUXILIADORA
GUAYNABO-AMERICAN MILITARY
BAYAMON-ACAD DISCIPULOS DE CRISTO
RIO PIEDRAS-COL SAN JOSE
RIO PIEDRAS-COL SAN ANTONIO
CAGUAS-NOTRE DAME HIGH SCHOOL
HUMACAO-COL SAN ANTONIO ABAD
ARECIBO-COL EVANG CAPITAN CORREA
RIO PIEDRAS-COL SAN IGNACIO
CABO ROJO-COL SAN AGUSTIN
BAYAMON-COL DE LA SALLE
PONCE-ACAD SANTA MARIA
MAYAGUEZ-ACAD LA INMACULADA
PONCE-COL SAN CONRADO
Escu
ela
s P
rivad
as
Tasa Graduación
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Figure 10. Top fourteen private high schools with the highest UPRM graduation ratesfor students who entered the School of Engineering in the cohorts of 1991-1997.
Performance of the students at UPRM’s College of Engineering
• Looking at the figures, we realized that the list of schools that meet the different criteria, were not the same.
• We saw a need to develop a function that include all the criteria. This function is based on the quadratic expected loss function.
• Therefore, these three indicators were combined to develop a performance index (PI) that will allow standard ratings of these high schools.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function
– The concept of quadratic loss function has been proposed by Phadke [2] to approximate quality losses.
– One can develop a performance index (PI) to compare high schools through the execution of their students at the high level institutions.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function
– The quadratic loss function is given by
– Usually in quality control applications, a tolerance Δ is defined such that if the y characteristic is within T + Δ (two sided tolerance) the characteristic is acceptable.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Loss(y) = k (y – T)2 (1)
where k is a proportionality constant and T is the target value for the y characteristic.
Definition of the Performance Index Using Quadratic Loss Function
– The quadratic loss function penalizes the behaviors that deviate from the target T.
– A challenge with the function is the definition of the constant k.
– Artiles-León [3] defined this value to assure that the loss function is not sensitive to the system of units used to measure the quality characteristic y.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function
– For the two sided tolerance problem this definition becomes: (2)
– Using k results in a “standardized” loss function. Since the standardized version of the loss function is dimensionless, if several quality characteristics are considered, their correspondent loss functions can be added.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
2
2
2
k
Definition of the Performance Index Using Quadratic Loss Function
– The quality characteristics or critical indicators that we are considering are:
• the average time to complete the BS degree
• the average graduation GPA
• the graduation rates for the high schools under consideration
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function
• These characteristics are not suited for the two sided tolerance approach.
• The first one, average time to degree, can be described better as an smaller-the-better characteristic, while the other two average GPA, and graduation rate of a higher-the-better characteristic form.
• Expanding the standardized concepts to one-sided tolerance characteristics the following two equations can be derived for smaller-the-better (3) and higher-the-better (4).
(3)
(4)
2
2
)(
y
ySLoss
2
2
)(y
ySLoss
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Definition of the Performance Index Using Quadratic Loss Function• A total standardized loss (TSLoss) for our case study can be defined
as:
(5)
where yi, and Δi corresponds to the characteristic and tolerance for the critical indicators.
23
23
22
22
21
21
yy
yTSLoss
Table 1. Ratings of High Schools Basedon Performance of Index
Using an Expected Loss Function to Identify Best High Schools for Recruitment
High School Performance Index
Colegio San Conrado, Ponce 3.250182
Academia de la Inmaculada Concepción, Mayagüez 3.376351
Secundaria UPR, Río Piedras 3.569336
Colegio San Antonio Abad, Humacao 3.737924
Patria Latorre, San Sebastian 3.74815
Academia Santa María, Ponce 3.796827
Colegio San Antonio, Río Piedras 3.893357
Notre Dame High School, Caguas 3.995966
Ramón José Dávila, Coamo 4.195212
Benito Cerezo, Aguadilla 4.237077
University Gardens, Río Piedras 4.326681
Ana Roque, Humacao 4.376365
Lola Rodríguez de Tió, San Germán 4.440817
Domingo Aponte Collazo, Lares 4.711063
Conclusions– Identifying the best high schools in the country allows
us to fulfill our mission of attracting the best possible prospective students to the College of Engineering.
– This is only a first step in fulfilling our mission. There are other strategies that we have to develop to enroll the best students.
– The loss function provides a scientific way to combine different criterion of performance to identify the best schools.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Future Work
– The suggested performance index, based on the TSLoss, should include additional critical indicators.
– We suggest exploring the following indicators, average GPA in math courses, average GPA in science courses, average GPA in language courses, attempted credits, among others.
– A limitation of the described performance index is that it does not take into account the correlations among the critical indicators variables considered.
– Techniques such as the Mahalanobis Distance to incorporate such relationships should be considered.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
References
[1] González-Barreto, D. and González-Quevedo, A.,“Attracting a More Diverse Student Population to the School of Engineering of the University of Puerto Rico at Mayagüez”, Proceedings of the 9th International Conference on Engineering Education. July 23-28, 2006. San Juan, PR, pp. R4E21, R4B25.
[2] Phadke, M. S., Quality Engineering using Robust Design, Prentice-Hall, Englewood Cliffs, NJ, 1989.
[3] Artiles-León, N., “A Pragmatic Approach to Multiple-Response Problems using Loss Functions”, Quality Engineering, 9,2, 1996-1997, pp. 213-220.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Acknowledgement
The authors want to acknowledge the assistance provided by Leo I. Vélez and Irmannette Torres from the Office of Institutional Research and Planning of the University of Puerto Rico at Mayagüez for providing and validating the data used in this study.
Using an Expected Loss Function to Identify Best High Schools for Recruitment
Using an Expected Loss Function to Identify Best High Schools for Recruitment