title: Latent class models for testing monotonicity and invariant item ordering for polytomous items.
abstract: Two assumptions that are relevant to many applications using item response theory are the assumptions of monotonicity (M) and invariant item ordering (IIO). A latent class model is proposed for ordinal items with inequality constraints on the class-specific item means. This model is used as a tool for testing for violations of M and IIO. A Gibbs sampling scheme is used for estimating the model parameters. It is shown that the deviance information criterion can be used as an overall test of M and IIO, while posterior predictive checks can be used to test these assumptions at the item level. A real data application illustrates a model-fitting strategy for detecting items that violate M and IIO.
authors.affiliation: University of Amsterdam, The Netherlands. r.ligtvoet@uva.nl
authors.forename: Rudy
authors.initials: R
authors.lastname: Ligtvoet
authors.forename: Jeroen K
authors.initials: JK
authors.lastname: Vermunt
mesh_terms: D001290:Attitude; D005260:Female; D006801:Humans; D015233:Models, Statistical; D012494:Sampling Studies; D011795:Surveys and Questionnaires; D014933:Women's Rights