Testing manifest monotonicity using order-constrained statistical inference

J. Tijmstra, D.J. Hessen, P.G.M. van der Heijden, K. Sijtsma

Research output: Contribution to journalArticleScientificpeer-review

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
Original languageEnglish
Pages (from-to)83-97
JournalPsychometrika
Volume78
Issue number1
DOIs
Publication statusPublished - 2013

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Statistical Inference
Monotonicity
Testing
Type I Error Rate
Latent Variables
Likelihood Ratio Test
p-Value
Homogeneity
Monotone
Simulation Study
Imply
Evaluate
Model
Simulation

Cite this

Tijmstra, J. ; Hessen, D.J. ; van der Heijden, P.G.M. ; Sijtsma, K. / Testing manifest monotonicity using order-constrained statistical inference. In: Psychometrika. 2013 ; Vol. 78, No. 1. pp. 83-97.
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Testing manifest monotonicity using order-constrained statistical inference. / Tijmstra, J.; Hessen, D.J.; van der Heijden, P.G.M.; Sijtsma, K.

In: Psychometrika, Vol. 78, No. 1, 2013, p. 83-97.

Research output: Contribution to journalArticleScientificpeer-review

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