Approximate Bayesian Techniques for Statistical Model Selection and Quantifying Model Uncertainty—Application to a Gait Study

Abstract

Frequently, biomedical researchers need to choose between multiple candidate statistical models. Several techniques exist to facilitate statistical model selection including adjusted R², hypothesis testing and p-values, and information criteria among others. One particularly useful approach that has been slow to permeate the biomedical literature is the notion of posterior model probabilities. A major advantage of posterior model probabilities is that they quantify uncertainty in model selection by providing a direct, probabilistic comparison among competing models as to which is the “true” model that generated the observed data. Additionally, posterior model probabilities can be used to compute posterior inclusion probabilities which quantify the probability that individual predictors in a model are associated with the outcome in the context of all models considered given the observed data. Posterior model probabilities are typically derived from Bayesian statistical approaches which require specialized training to implement, but in this paper we describe an easy-to-compute version of posterior model probabilities and inclusion probabilities that rely on the readily-available Bayesian information criterion. We illustrate the utility of posterior model probabilities and inclusion probabilities by re-analyzing data from a published gait study investigating factors that predict required coefficient of friction between the shoe sole and floor while walking.