title: Evaluating Manifest Monotonicity Using Bayes Factors.
abstract: The assumption of latent monotonicity in item response theory models for dichotomous data cannot be evaluated directly, but observable consequences such as manifest monotonicity facilitate the assessment of latent monotonicity in real data. Standard methods for evaluating manifest monotonicity typically produce a test statistic that is geared toward falsification, which can only provide indirect support in favor of manifest monotonicity. We propose the use of Bayes factors to quantify the degree of support available in the data in favor of manifest monotonicity or against manifest monotonicity. Through the use of informative hypotheses, this procedure can also be used to determine the support for manifest monotonicity over substantively or statistically relevant alternatives to manifest monotonicity, rendering the procedure highly flexible. The performance of the procedure is evaluated using a simulation study, and the application of the procedure is illustrated using empirical data.
authors.affiliation: Department of Methodology and Statistics, Faculty of Social and Behavioral Sciences, Tilburg University, PO Box 90153, 5000 LE , Tilburg, The Netherlands. j.tijmstra@uvt.nl.|CITO, NATIONAL Institute for Educational Measurement, Arnhem, The Netherlands. j.tijmstra@uvt.nl.
authors.forename: Jesper
authors.initials: J
authors.lastname: Tijmstra
authors.affiliation: CITO, NATIONAL Institute for Educational Measurement, Arnhem, The Netherlands.|Utrecht University CITO, NATIONAL Institute for Educational Measurement, Utrecht, The Netherlands.
authors.forename: Herbert
authors.initials: H
authors.lastname: Hoijtink
authors.affiliation: Tilburg University, Tilburg, The Netherlands.
authors.forename: Klaas
authors.initials: K
authors.lastname: Sijtsma
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D015233:Models, Statistical; D011594:Psychometrics / Q000706:statistics & numerical data
keywords: Bayes factor; essential monotonicity; item response theory; latent monotonicity; manifest monotonicity