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Abstract
This paper introduces Bayesian analysis and demonstrates its application to parameter estimation of the logistic regression via Markov Chain Monte Carlo (MCMC) algorithm. The Bayesian logistic regression estimation is compared with the classical logistic regression. Both the classical logistic regression and the Bayesian logistic regression suggest that higher per capita income is associated with free trade of countries. The results also show a reduction of standard errors associated with the coefficients obtained from the Bayesian analysis, thus bringing greater stability to the coefficients. It is concluded that Bayesian Markov Chain Monte Carlo algorithm offers an alternative framework for estimating the logistic regression model.
Highlights
In applied econometrics research, non linear models are essential tools for analysing empirical data
Both the classical logistic regression and the Bayesian logistic regression suggest that higher per capita income is associated with free trade of countries
All the mass of the posterior distributions of the per capita income are in the positive as illustrated in the plots of their posterior distributions in figure 1 in appendix I. These observations lead to the conclusion that higher per capita income is associated with free trade of countries
Summary
Non linear models are essential tools for analysing empirical data. The application of the logistic regression to binary response data is simple to understand, easy to compute and widely used This classical approach fits the logistic regression by means of an iterative procedure such as the maximum likelihood, and inferences about the model are based on asymptotic theory. Progress in Markov Chain Monte Carlo (MCMC) methods has made it possible to fit various non linear regression models. Irrespective of these developments, few studies have employed the MCMC based approach to model the logistic regression. The aim of this study is to introduce Bayesian analysis and demonstrates its application to parameter estimation of the logistic regression via Markov Chain Monte Carlo (MCMC) algorithm. This study presents a comparison of the Bayesian logistic regression with the classical logistic regression
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