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.