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Journal of Statistics Applications & Probability

Author Country (or Countries)

South Africa

Abstract

The misuse of alcohol and drugs is a continuous life threat globally, including in South Africa. For that reason, researchers continue to investigate the risk factors associated with alcohol and drugs misuse. Most studies in literature employed the classical logistic regression model to investigate these risk factors. However, some of the issues pertaining to the classical methods are accounted for in the Bayesian framework. Likewise, the Bayesian logistic regression model can also account for problematic issues to the classical logistic regression model. Several studies used the Bayesian logistic regression model to investigate the risk factors associated with alcohol and drugs misuse. Usually, most Bayesian studies utilize default prior probability distributions such as Jeffereys’ prior and Zellner’s informative g-prior distributions. Not long ago, modified versions of Zellner’s informative g-prior distribution have been proposed. This study aims to evaluate the effectiveness of a modified Zellner’s informative g-prior distribution and subdue separation in modelling the misuse of alcohol and drugs. The model developed through the use of a modified Zellner’s g-prior distribution is compared to the models developed through the use of a hyper g-prior distribution and mixtures of g and n prior distribution. Comparisons are based on precision and average prediction error. Although the models yielded similar results, the modified version of Zellner’s informative g-prior distribution resulted in narrow credible intervals, and a small everage prediction error. Separation is also accounted for in the model. In this study, the modified version of Zellner’s informative g-prior distribution is evidently effective. All models are developed using the Bayesian adaptive sampling (BAS) R package. Further research may include evaluating some of the recommended prior distributions for the Generalised Linear Models (GLM) and comparison of Bayesian binary logistic regression developed in this study with logistic regression in Machine Learning algorithms.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/120233

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