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, 78, (1), pp. 83-97. (doi:10.1007/s11336-012-9297-x). (PMID:25107519).


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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
Digital Object Identifier (DOI): doi:10.1007/s11336-012-9297-x
ISSNs: 0033-3123 (print)
Keywords: item response theory, latent monotonicity, manifest monotonicity, monotone homogeneity model, order-constrained statistical inference
Organisations: Statistical Sciences Research Institute
ePrint ID: 344614
Date :
Date Event
6 December 2012Published
Date Deposited: 24 Oct 2012 15:49
Last Modified: 17 Apr 2017 16:26
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/344614

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