Heck DW, Davis-Stober CP. Multinomial Models with Linear Inequality Constraints: Overview and Improvements of Computational Methods for Bayesian Inference.
JOURNAL OF MATHEMATICAL PSYCHOLOGY 2019;
91:70-87. [PMID:
30956351 PMCID:
PMC6448806 DOI:
10.1016/j.jmp.2019.03.004]
[Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
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.
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