Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

Jesper Tijmstra (), David Hessen, Peter Heijden and Klaas Sijtsma

Psychometrika, 2013, vol. 78, issue 1, 83-97

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. Copyright The Psychometric Society 2013

Keywords: item response theory; latent monotonicity; manifest monotonicity; monotone homogeneity model; order-constrained statistical inference (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11336-012-9297-x

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