Evaluating Multinomial Order Restrictions With Bridge Sampling

Translational Abstract When researchers evaluate categorical variables, their hypotheses typically postulate that all category proportions are exactly equal or equal to fixed values. These hypotheses can be evaluated using standard tests. However, whenever researchers postulate hypotheses that entail expectations about increasing or decreasing trends, they must rely on methods that are relatively inefficient and computationally expensive. To address this problem we developed a bridge sampling routine that allows an efficient evaluation of these trends for multinomial variables. An empirical application showcases that bridge sampling outperforms current Bayesian methods. The method is extended so that hypotheses can also include mixtures between equality and inequality constraints. Hypotheses concerning the distribution of multinomial proportions typically entail exact equality constraints that can be evaluated using standard tests. Whenever researchers formulate inequality constrained hypotheses, however, they must rely on sampling-based methods that are relatively inefficient and computationally expensive. To address this problem we developed a bridge sampling routine that allows an efficient evaluation of multinomial inequality constraints. An empirical application showcases that bridge sampling outperforms current Bayesian methods, especially when relatively little posterior mass falls in the restricted parameter space. The method is extended to mixtures between equality and inequality constrained hypotheses.