Multi-level random coefficient regression models to examine students' scholastic achievement by gender, class and locality

Abstract

Multilevel models, also known as hierarchical linear models or random coefficient models are more complex than traditional regression models and need careful specification. These models are primarily used for the analysis of data with complex patterns of variability, with a focus on nested sources of variability and involve the measurements of variables of more than one level of hierarchy. A common and obvious hierarchy consists of students nested in school classes, and classes nested in locality schools. For such data, it is usually necessary to consider the variability associated with each level of nesting. The aim of this dissertation is to help understand how final examination mathematics marks obtained by first year Junior Lyceum students attending different schools differ by class, gender and locality. Several models that predict the Mathematics marks are presented. These include an ANOVA regression model, a two-level random intercept model, a two-level random coefficient model as well as a three-level random intercept model. These models are contrasted and assessed using several diagnostic tools.