Analyzing cross-sectional data related to student engagement using GLMs and hierarchical random coefficient models

Abstract

Regression analysis plays a central role in statistics being one of its most powerful and commonly used techniques. The standard linear regression models assume that the response variable is normal. However; it is not always the case. A wide variety of models with a categorical response is a typical example, where the assumption of normality cannot be accepted as reasonable. The generalized linear model framework was introduced in 1972 by J. Nelder and R. Wedderburn in the paper Generalized linear models (Journal of the Royal Statistical Society, Series A). Generalized linear models are designed to overcome the limitations of regression models by accommodating any distribution that is a member of the exponential family. Moreover, these models also allow transformation of the response variable through the link function. GLM models are fitted to relate an engagement score to four student contextual variables, particularly MICI (Motivational Instructional Context), Teacher Support, Parent Support and Peer Support. However, GLMs require independence of the observations. Hence repeated measurements on the same subject or over time induce correlations which cannot adequately be analyzed within the GLM framework. An approach that may overcome this limitation is multilevel modeling which provides a powerful framework for exploring how average relationships vary across the hierarchical structure of the study design. As well as allowing the relationship between the explanatory variables and dependent variables to be estimated, multilevel models also known as random coefficient models enable the extent of variation in the outcome of interest to be measured at each level of nesting. The data set entails observations, which are the student engagement scores nested within the forms (level-2 units). The study produces multilevel models to investigate and predict student outcomes. In the students' affective, behavior and academic aspects. It comprises of three random coefficient models, each with two levels of nesting.