A Multinomial Logistic Model for the Higher Education Value-Added with K-means Clustering

Abstract

The implementation of state tests at the end of the different academic cycles, to pursue high standard education, is used by many countries in the world. For the Colombian case there are two classic exams: one of them is for all the students that are about to finish high school, called Saber 11, and the other one is for people that are finishing the university cycle, called Saber Pro. Both are measured by quantitative scores. This case study was considered because it was possible to know the Saber 11 and Saber Pro scores for the same individual. The machine learning k-means technique was used for defining different groups of Saber Pro scores. Then a multinomial logistic model was applied to estimate the probability of a student to fall in every one of those groups, given his own characteristics. In other words, the distribution probability of the Saber Pro results was produced through the different defined groups using k-means. This splitting technique is far better than the standard even subdivisions (like quartiles or quintiles), because it produces optimal distance-wise clusters that allows more natural statistical results. This work gives numerical insights regarding the performance for different student profiles, and shows that the educational achievement at the end of an academic program, is influenced by the initial academic level, the socioeconomic condition, and the university status, but also that more input variables must be analyzed and included. In particular, for the considered samples, the research concluded that the individuals with the least favorable socioeconomic condition have a tendency to underperform when compared with the rest of the population, and the students of the non-accredited institutions tend to obtain lower educational achievements than the accredited ones. Of course, in all the investigated groups, students with a high result in Saber 11 tend to achieve an outstanding performance in Saber Pro, regardless of their socioeconomic status or the accreditation status of the institution. On the other hand, the gender shows no general behavior or whatsoever.