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The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions

Published online by Cambridge University Press:  01 January 2025

Dylan Molenaar*
Affiliation:
University of Amsterdam
Conor V. Dolan
Affiliation:
University of Amsterdam
Paul de Boeck
Affiliation:
University of Amsterdam
*
Requests for reprints should be sent to Dylan Molenaar, Psychological Methods, Department of Psychology, University of Amsterdam, Weesperplein 4, 1018 XA, Amsterdam, The Netherlands. E-mail: d.molenaar@uva.nl

Abstract

The Graded Response Model (GRM; Samejima, Estimation of ability using a response pattern of graded scores, Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, θ, to underlie the ordinal item scores (Takane & de Leeuw in Psychometrika, 52:393–408, 1987). Traditionally, a normal distribution is specified for Z implying homoscedastic error variances and a normally distributed θ. In this paper, we present the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastic error variances and a skew-normal latent trait. An appealing property of the extended GRM is that it includes the traditional GRM as a special case. This enables specific tests on the normality assumption of Z. We show how violations of normality in Z can lead to asymmetrical category response functions. The ability to test this normality assumption is beneficial from both a statistical and substantive perspective. In a simulation study, we show the viability of the model and investigate the specificity of the effects. We apply the model to a dataset on affect and a dataset on alexithymia.

Type
Original Paper
Copyright
Copyright © 2012 The Psychometric Society

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