Spatio-Temporal Modeling of the Kenya Certificate of Primary Education pupil scores through a Bayesian approach

Abstract

This project presents a spatio-temporal model for pupil performance in Kenya certificate Of Primary Education (KCPE) in Kenya between 2006 and 2010 in the 47 counties of Kenya. For this analysis, time will be represented by year (2006-2010) while space will be represented by county. The goal of the project is to put forward an efficient estimation and prediction approach that accounts for both spatial and temporal dependence. The model employs a Bayesian method in which a prior distribution and a likelihood are stated and consequently updated using the data. The model involves a Gaussian Field (GF), affected by a measurement error and a process characterized by time and space. Data used for this study refers to the KCPE scores of all primary schools in the 47 counties of Kenya from 2006 to 2010. A dependent variable (DV) is created by obtaining aggregate counts of the number of students scoring 350 marks and above in KCPE in each county over the five-year period. Analysis was done using INLA, an R package that makes use of deterministic nested Laplace approximations to provide a faster and more accurate alternative to Markov Chain Monte Carlo (MCMC) methods. A negative binomial likelihood was assigned to the DV, and, together with a Gaussian prior, space and time attributes were used in a model for explaining performance in KCPE over the five year period and within the 47 counties. From the analysis, it was found out that throughout the five-year period, the best performance was recorded in 2008. Generally, students in counties located in the central part of the country have the highest probability of scoring at least 350 marks in KCPE while those in the lake and coast regions have the lowest probability. Additionally, performance in any county was seen to be related to that of neighboring counties and the relation became weaker as the distance increases