Abstract
In statistical modelling studies, due to the advanced technology and methodological developments, it is possible to construct alternative models assumed to generate the data. Therefore, the process of choosing “the best model” among available competing models appears to be one of the crucial steps that has to be included in the modelling process. In this study, Bayes factor, which is a preferred Bayesian approach to the solution of statistical model selection problem, is introduced. For the cases when analytical computation of Bayes factor is not possible, in addition to Bayesian Information Criterion (BIC), Carlin and Chib method based on Markov Chain Monte Carlo (MCMC) simulation is explained. Besides, a frequently used criteria in the recent years of model selection applications, namely Deviance Information Criterion (DIC), which has a completely different working principle than Bayes factor, is described in detail. Two models appeared in the literature as a result of an application of quantal modelling, which is an example of a semi-parametric modelling, are compared by means of Bayes factor, BIC and DIC.