1. Sonia M. Bartolomei-Suárez Associate Dean of Academic Affairs, School of Engineering David González-Barreto Professor, Industrial Engineering Department Antonio González-Quevedo Professor, Civil Engineering and Surveying Department University of Puerto Rico, Mayagüez 5/4/2015 Using an Expected Loss Function to Identify Best High Schools for Recruitment

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. Figure 1. First 15 Public High Schools with 50 or more graduates at UPRM for the College of Engineering (Years 1995-2005).

9. 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).

10. 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.

11. 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.

12. 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

13. Figure 5. Top 15 public high schools with the lowest average time to complete the bachelor’s degree in engineering (1991-2006).

14. 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).

15. 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).

16. 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).

17. 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.

18. Using an Expected Loss Function to Identify Best High Schools for Recruitment Figure 10. Top fourteen private high schools with the highest UPRM graduation rates for students who entered the School of Engineering in the cohorts of 1991-1997.

19. 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

20. 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

21. 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.

22. 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

23. 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

24. 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

25. 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)

26. 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.

27. Table 1. Ratings of High Schools Based on Performance of Index Using an Expected Loss Function to Identify Best High Schools for Recruitment High School Performance Index Colegio San Conrado, Ponce3.250182 Academia de la Inmaculada Concepción, Mayagüez3.376351 Secundaria UPR, Río Piedras3.569336 Colegio San Antonio Abad, Humacao3.737924 Patria Latorre, San Sebastian3.74815 Academia Santa María, Ponce3.796827 Colegio San Antonio, Río Piedras3.893357 Notre Dame High School, Caguas3.995966 Ramón José Dávila, Coamo4.195212 Benito Cerezo, Aguadilla4.237077 University Gardens, Río Piedras4.326681 Ana Roque, Humacao4.376365 Lola Rodríguez de Tió, San Germán4.440817 Domingo Aponte Collazo, Lares4.711063

28. 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

29. 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

30. 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

31. 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