Constant latent odds-ratios models and the mantel-haenszel null hypothesis |
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Authors: | Email author" target="_blank">David?J?HessenEmail author |
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Institution: | (1) Department of Psychology, University of Amsterdam, Roetersstraat 15, 1018, WB, Amsterdam, The Netherlands |
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Abstract: | In the present paper, a new family of item response theory (IRT) models for dichotomous item scores is proposed. Two basic
assumptions define the most general model of this family. The first assumption is local independence of the item scores given
a unidimensional latent trait. The second assumption is that the odds-ratios for all item-pairs are constant functions of
the latent trait. Since the latter assumption is characteristic of the whole family, the models are called constant latent
odds-ratios (CLORs) models. One nonparametric special case and three parametric special cases of the general CLORs model are
shown to be generalizations of the one-parameter logistic Rasch model. For all CLORs models, the total score (the unweighted
sum of the item scores) is shown to be a sufficient statistic for the latent trait. In addition, conditions under the general
CLORs model are studied for the investigation of differential item functioning (DIF) by means of the Mantel-Haenszel procedure.
This research was supported by the Dutch Organization for Scientific Research (NWO), grant number 400-20-026. |
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Keywords: | IRT odds-ratio sufficient statistic weak item independence manifest monotonicity Rasch model DIF Mantel-Haenszel procedure |
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