A Comparison of Bayes Factor Approximation Methods Including Two New Methods

Abstract

Bayes factors (BFs) play an important role in comparing the fit of statistical models. However, computational limitations or lack of an appropriate prior sometimes prevent researchers from using exact BFs. Instead, it is approximated, often using the Bayesian Information Criterion (BIC) or a variant of BIC. The authors provide a comparison of several BF approximations, including two new approximations, the Scaled Unit Information Prior Bayesian Information Criterion (SPBIC) and Information matrix-based Bayesian Information Criterion (IBIC). The SPBIC uses a scaled unit information prior that is more general than the BIC’s unit information prior, and the IBIC utilizes more terms of approximation than the BIC. Through simulation, the authors show that several measures perform well in large samples, that performance declines in smaller samples, and that SPBIC and IBIC provide improvement to existing measures under some conditions, including small sample sizes. The authors illustrate the use of the fit measures with the crime data of Ehrlich and then conclude with recommendations for researchers.