Analyzing longitudinal count data related to re-sits in the faculty of science using GLMs and hierarchical poisson random coefficient models

Abstract

The GLM family subsumes a large number of statistical models that are widely used in practical applications for prediction purposes. GLMs overcome the limitations of traditional Regression models, which assume a Normal distribution for the responses. In this thesis, we present three GLMs to forecast the number of ECTS resits for students in the Faculty of Science. The first model is a Normal regression model that is plagued by model misspecifications. The second and third models improve the model fit by assuming a Poisson and Gamma distribution that respectively lead to the logarithmic and reciprocal canonical link functions. Three predictors were identified that were thought to contribute considerably in explaining the variability in the responses. These include the University entry qualification score, the subjects studied and the year in which the ECTS resit count was recorded. A limitation of GLMs is that they assume independence for the responses. It is very implausible that responses from longitudinal data are independent. An approach that overcomes this limitation is based on considering the hierarchical structure of the study design. Multilevel models, also known as random coefficient models, focus on nested sources of variability and involve measurements of variables for more than one level of hierarchy. Our data set comprise responses (number of ECTS resits) that are nested within the students (level-2 units) and students that are nested within departments (level 3 units). The data is appropriate for multilevel modelling. In this dissertation, we present four multilevel models to forecast the number of ECTS resits for B.Sc.(Hons.) students. These include a random intercept and a random coefficient model each with two and three levels of nesting.