  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.
