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Testing Manifest Monotonicity Using Order-Constrained Statistical Inference

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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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Authors and Affiliations

  1. Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht Univeristy, PO Box 80140, 3508 TC, Utrecht, The Netherlands

    Jesper Tijmstra, David J. Hessen & Peter G. M. van der Heijden

  2. Tilburg University, Tilburg, The Netherlands

    Klaas Sijtsma

Authors
  1. Jesper Tijmstra
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  2. David J. Hessen
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  3. Peter G. M. van der Heijden
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  4. Klaas Sijtsma
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Correspondence to Jesper Tijmstra.

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Tijmstra, J., Hessen, D.J., van der Heijden, P.G.M. et al. Testing Manifest Monotonicity Using Order-Constrained Statistical Inference. Psychometrika 78, 83–97 (2013). https://doi.org/10.1007/s11336-012-9297-x

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  • DOI: https://doi.org/10.1007/s11336-012-9297-x

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