Title: Bayes Factors for Testing Ordinal Constrained Hypotheses in Categorical
Data
Authors: Alexandra Sarafoglou, Alexander Ly, Quentin Gronau, Erik-Jan van
Kesteren, Eric-Jan Wagenmakers, Maarten Marsman
Affiliation: University of Amsterdam; Centrum Wiskunde & Informatica;
University of Utrecht
Abstract:
Researchers often approach the analysis of categorical data already expecting
certain relations between the probabilities of the categorical events. For
instance, the key assumption of item response theory - latent monotonicity -
is an example for ordinal expectations.
Researchers are able to adequately capture their expectations and formalize
them into testable hypotheses by stipulating ordinal constraints on the
parameters of interest. The Bayesian framework includes several methods to
evaluate these hypotheses using Bayes factors, i.e., the encompassing prior
approach (Klugkist, Kato, & Hoijtink, 2005), or the conditioning method
(Mulder et al., 2009). These methods, however, are potentially unstable and
time-consuming if the number of categories increases.
We introduce an accurate and fast alternative for testing ordinal constrained
hypotheses in categorical data. Our approach is based on the bridge sampling
method proposed by Bennet (1976) and Meng and Wong (1996). By means of a
concrete example, we will showcase the method in the user-friendly and
open-source software JASP.