Testing manifest monotonicity using order-constrained statistical inference
Tijmstra,J. Hessen,D.J. van der Heijden,P.G.M. Sijtsma,K.
Tijmstra,J.
Hessen,D.J.
van der Heijden,P.G.M.
Sijtsma,K.
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. Keywords: item response theory, latent monotonicity, manifest monotonicity, monotone homogeneity model, order-constrained statistical inference
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2013
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Research Projects
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Tijmstra, J, Hessen, D J, van der Heijden, P G M & Sijtsma, K 2013, 'Testing manifest monotonicity using order-constrained statistical inference', Psychometrika, vol. 78, no. 1, pp. 83-97. https://doi.org/10.1007/s11336-012-9297-x