Testing manifest monotonicity using order-constrained statistical inference

Tijmstra, J.D., Hessen, D.J., van der Heijden, P.G.M. and Sijtsma, K. (2012) Testing manifest monotonicity using order-constrained statistical inference. Psychometrika, 78 (1), 83-97. (doi:10.1007/s11336-012-9297-x). (PMID:25107519)

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.

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Contributors

Author: P.G.M. van der Heijden

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