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 (In Press).
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Description/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.
| Item Type: | Article |
|---|---|
| ISSNs: | 0033-3123 (print) 1860-0980 (electronic) |
| Related URLs: | |
| Keywords: | item response theory, latent monotonicity, manifest monotonicity, monotone homogeneity model, order-constrained statistical inference |
| Subjects: | H Social Sciences > HA Statistics |
| Divisions: | Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute |
| Item ID: | 344614 |
| Date Deposited: | 24 Oct 2012 15:49 |
| Last Modified: | 24 Oct 2012 15:50 |
| Contributors: | Tijmstra, J.D. (Author) Hessen, D.J. (Author) van der Heijden, P.G.M. (Author) Sijtsma, K. (Author) |
| Date: | 2012 |
| Status: | In Press |
| URI: | http://eprints.soton.ac.uk/id/eprint/344614 |
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