Multinomial Models with Linear Inequality Constraints: Overview and Improvements of Computational Methods for Bayesian Inference

TL;DR

This paper reviews and improves computational methods for Bayesian inference in multinomial models with linear inequality constraints, providing efficient algorithms and an R package for practical application.

Contribution

It introduces a general Gibbs sampler and alternative methods for Bayesian analysis of constrained multinomial models, along with an accessible R package.

Findings

Developed a Gibbs sampler for constrained Bayesian inference.

Summarized alternative methods for Bayes factor estimation.

Provided an R package 'multinomineq' for implementation.

Abstract

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices). For both representations, we describe a general Gibbs sampler for drawing posterior samples in order to carry out Bayesian analyses. We also summarize alternative sampling methods for estimating Bayes factors for these model representations using the encompassing Bayes factor method. We introduce the R package multinomineq, which provides an easily-accessible interface to a computationally efficient implementation of these techniques.