multibridge: An R Package To Evaluate Informed Hypotheses in Binomial and Multinomial Models

The multibridge R package allows a Bayesian evaluation of informed hypotheses H_r 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 theta: (a) hypotheses that postulate equality constraints (e.g., theta_1 = theta_2 = theta_3); (b) hypotheses that postulate inequality constraints (e.g., theta_1 < theta_2 theta_2 > theta_3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., theta_1 < theta_2 = theta_3); and (d) hypotheses that postulate combinations of (a)--(c) (e.g., theta_1 < theta_2 = theta_3, theta_4). Any informed hypothesis H_r may be compared against the encompassing hypothesis H_e that all category proportions vary freely, or against the null hypothesis H_0 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.