Multibridge: an R package to evaluate informed hypotheses in binomial and multinomial models

Abstract

The multibridge R package allows a Bayesian evaluation of informed hypotheses [Formula: see text] applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions 𝜃: (a) hypotheses that postulate equality constraints (e.g., 𝜃₁ = 𝜃₂ = 𝜃₃); (b) hypotheses that postulate inequality constraints (e.g., 𝜃₁ < 𝜃₂ < 𝜃₃ or 𝜃₁ > 𝜃₂ > 𝜃₃); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., 𝜃₁ < 𝜃₂ = 𝜃₃); and (d) hypotheses that postulate combinations of (a)-(c) (e.g., 𝜃₁ < (𝜃₂ = 𝜃₃),𝜃₄). Any informed hypothesis [Formula: see text] may be compared against the encompassing hypothesis [Formula: see text] that all category proportions vary freely, or against the null hypothesis [Formula: see text] that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

Keywords: Bayes factors; Bridge sampling; Inequality constraints; Model selection; Savage-Dickey density ratio.