title: Testing manifest monotonicity using order-constrained statistical inference.
abstract: Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores, such as the restscore, a single item score, and in some cases the total score. In this study, we show that manifest monotonicity can be tested by means of the order-constrained statistical inference framework. We propose a procedure that uses this framework to determine whether manifest monotonicity should be rejected for specific items. This approach provides a likelihood ratio test for which the p-value can be approximated through simulation. A simulation study is presented that evaluates the Type I error rate and power of the test, and the procedure is applied to empirical data.
authors.affiliation: Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht Univeristy, PO Box 80140, 3508 TC, Utrecht, The Netherlands, j.tijmstra@uu.nl.
authors.forename: Jesper
authors.initials: J
authors.lastname: Tijmstra
authors.forename: David J
authors.initials: DJ
authors.lastname: Hessen
authors.forename: Peter G M
authors.initials: PG
authors.lastname: van der Heijden
authors.forename: Klaas
authors.initials: K
authors.lastname: Sijtsma
mesh_terms: D006801:Humans; D011594:Psychometrics / Q000379:methods*; D013223:Statistics as Topic / Q000379:methods*
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