We present a new method for jointly modelling the students' results in the university's admission exams and their performance in subsequent courses at the university. The case considered involved all the students enrolled at the University of Campinas in 2014 to evening studies programs in educational branches related to exact sciences. We collected the number of attempts used for passing the university course of geometry and the results of the admission exams of those students in seven disciplines. The method introduced involved a combination of multivariate generalised linear mixed models (GLMM) and graphical models for representing the covariance structure of the random components. The models we used allowed us to discuss the association of quantities of very different nature. We used Gaussian GLMM for modelling the performance in the admission exams and a frailty discrete-time Cox proportional model, represented by a GLMM, to describe the number of attempts for passing Geometry. The analyses were stratified into two populations: the students who received a bonus giving advantages in the university's admission process to compensate social and racial inequalities and those who did not receive the compensation. The two populations presented different patterns. Using general properties of graphical models, we argue that, on the one hand, the predicted performance in the admission exam of Mathematics could solely be used as a predictor of the performance in geometry for the students who received the bonus. On the other hand, the Portuguese admission exam's predicted performance could be used as a single predictor of the performance in geometry for the students who did not receive the bonus.
翻译:在大学入学考试和随后大学课程中,我们提出了共同模拟学生成绩的新方法,在大学入学考试和学生成绩的随后课程中,这个案例涉及坎皮纳斯大学2014年注册的所有学生到与精确科学有关的教育分支的夜校学习课程;我们收集了大学几何课程的尝试次数和这些学生在七个学科的入学考试结果;采用的方法包括多种变式一般线性混合模型(GLMM)和代表随机组成部分差异结构的图形模型。我们使用的模型允许我们讨论不同性质数量的关系。我们使用高西安GLMMM模型模拟入学考试成绩和以GLMM为代表的脆弱、不固定的考克斯比例模型,以描述通过几何学考试的尝试次数;分析分为两类:在大学入学过程中获得奖励的学生可以弥补社会和种族不平等,而没有获得补偿的学生则可以享受到这些奖赏。两个群体展示了不同类型。我们用Gausian GLMMMMM模型来模拟入学成绩的模型的一般属性,我们用一个预测的成绩来预测数学成绩。我们用一个手算的成绩。