Neutrosophic Generalised Linear Mixed Effects Modelling of Basic Schools Performance

Abstract

In this thesis, a six-parameter alternative to the Generalised Linear Model was developed to account for nonnormality, unobserved factors in the form of random effect, interdependence of and heterogeneity among respondents. The techniques used included a novel hybrid of neutrosophic statistics, principal component analysis, and generalized mixed effect modeling. The robustness of the developed model was verified through sample variation, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The Model was tested with Ghana’s educational dataset to explain the achievement gaps among private and public school students in the BECE with 70% used for training and 30% as validation set. The model's estimations found that the random effect parameter had a significant effect on achievement gap, explaining around 9% of variability across people across all factors. According to the magnitude rank of predicted probability of the model, the top five variables influencing the performance gap between students attending private and public schools show that Administrative-Logistic causes account for 80% of the variance. These were listed in order of increasing importance: Daily Quality Supervision of Head teacher and Head teacher supervision by school proprietors, Timely Delivery of Books and Learning Materials by Parents/Stakeholders for Students; Conducive Teaching/Learning Environment; Concern and Parental Support for Students Academic Output (PTA). In conclusion, the proposed modified version in this research is recommended over the existing generalised linear models for educational research due to its robustness. Based on the findings of this research it is recommended that educational stakeholders consider the major determinants of this research that significantly affects BECE performance to maximise teaching and learning in Ghana’s Basic schools.