Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

• Published in: Journal of mathematical psychology 2019-08, Vol.91, p.70-87
• Main Authors: Heck, Daniel W., Davis-Stober, Clintin P.
• Format: Article
• Language: English
• Subjects: Bayes factor; Bayesian model selection; Convex polytope; Gibbs sampling; Order constraints
• ISSN: 0022-2496; 1096-0880
• DOI: 10.1016/j.jmp.2019.03.004

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. •Psychological theory often leads to inequality-constrained multinomial models.•Constraints are defined by inequalities or the convex hull of a set of vertices.•We develop a Gibbs sampler for Bayesian estimation using either representation.•We offer improved methods for model testing using the encompassing Bayes factor.•The R package multinomineq implements the proposed methods.