An Extended Six-parameter Generalised Linear Mixed Effects Model for Achievement Gaps among Public and Private Basic Schools of Ghana

Abstract

The mixed generalized linear model extension has distinct advantages over generalised linear models and hierarchical linear models by reducing estimation and precision errors, and increasing power. This paper aimed at building a six parameter Generalised Mixed linear Model with five structural parameters that explain students, teachers, and administrative-logistic characteristics and interaction effects as well as random effect parameter. Our model, which has Bernoulli response, and Logit link function outperformed existing models and was robust across varied sample sizes on the basis of AIC and BIC. Parameters of the model were estimated by Maximum Likelihood Estimation Method. The nonparametric contour-3D stratification was used to compare performance of public and private school pupils directly with respect to their BECE performance under each element of a given factor at a time. Our advanced model simultaneously takes into account the variance as a result of the relatively small samples taken from each category of private school as well as any bias that may have been introduced by the different participation rates between the private and public-school categories. Our model identified class competition, concern and parental support for their children's academic output, timely provision of books and learning materials for students, daily quality supervision of the head teacher and teacher by superiors, and conducive teaching and learning environments as the leading causes of performance gaps in the BECE examination in Ghana. It is recommended for the inferences made in this paper to be used by stake-holders of the basic schools to help optimise teaching and learning processes which will in the long run enhance performance of the pupils in the BECE examination.