A longitudinal study that analyzes student performance in primary schools using generalized linear models, repeated measure analysis and multilevel modelling

Abstract

Normal regression models are widely used in applications since they provide versatile statistical tools for studying the relationship between a dependent variable and one or more independent variables. However, they are not flexible enough to implement models that do not follow a normal distribution. Generalized linear models overcome the limitations of Normal regression models and accommodate any distribution that is a member of the exponential family. GLMs also allow the transformation of the response variable through the link function. Logistic regression models are special GLMs for categorical response variables where a Binomial distribution and a logit link function are assumed. This probability model is used to predict the 'outcome' indicating whether the student will enter a Junior Lyceum. One of the assumptions of GLMs is that the responses are independent. However, it is very unlikely that responses from longitudinal data are independent and so the GLM framework may not be so appropriate. Longitudinal data, often called repeated measurements arise when units provide responses on multiple occasions. Two important features of longitudinal data are the clustering of responses within units and the chronological ordering of responses. Longitudinal designs allow the separation of cross-sectional and longitudinal effects. There are two approaches to modelling longitudinal data. One approach is a repeated measurements analysis of variance that allows explicitly the selection of a plausible variance covariance structure. The second approach is multilevel modelling which provides a powerful framework for exploring how average relationships vary across the hierarchical structure of the study design. These statistical procedures were used to analyze a data set comprising the marks of a number of Gozitan students in Mathematics, English and Maltese over the last three years in primary schools. Other explanatory variables include the gender and type of school attended by the student.