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

Abstract

The multibridgeR package allows a Bayesian evaluation of informed hypotheses Hr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathscr{H}}_{r}$\\end{document} 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 \U0001d703: (a) hypotheses that postulate equality constraints (e.g., \U0001d7031 = \U0001d7032 = \U0001d7033); (b) hypotheses that postulate inequality constraints (e.g., \U0001d7031 < \U0001d7032 < \U0001d7033 or \U0001d7031 > \U0001d7032 > \U0001d7033); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., \U0001d7031 < \U0001d7032 = \U0001d7033); and (d) hypotheses that postulate combinations of (a)–(c) (e.g., \U0001d7031 < (\U0001d7032 = \U0001d7033),\U0001d7034). Any informed hypothesis Hr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathscr{H}}_r$\\end{document} may be compared against the encompassing hypothesis He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathscr{H}}_e$\\end{document} that all category proportions vary freely, or against the null hypothesis H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}${\\mathscr{H}}_{0}$\\end{document} 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.