Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

TL;DR

This paper introduces a Bayesian model selection method for categorical data using encompassing priors and importance sampling, enabling effective comparison of models with complex constraints on logits and interactions.

Contribution

It presents a novel Bayesian framework combining encompassing priors and importance sampling for model selection in constrained marginal models for categorical data.

Findings

Effective model selection demonstrated on real datasets

Bayes factors estimated accurately via importance sampling

Sensitivity analysis shows robustness to prior choices

Abstract

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits (local, global, continuation or reverse continuation), generalised log-odds ratios and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is formulated following the encompassing prior approach. Then, model selection is performed by using Bayes factors which are estimated by an importance sampling method. The approach is illustrated through three applications involving some datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also considered.