title: The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions.
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.
authors: Psychological Methods, Department of Psychology, University of Amsterdam, Weesperplein 4, 1018 XA, Amsterdam, The Netherlands. d.molenaar@uva.nl.
authors: Dylan
authors: D
authors: Molenaar
authors: Psychological Methods, Department of Psychology, University of Amsterdam, Weesperplein 4, 1018 XA, Amsterdam, The Netherlands.
authors: Conor V
authors: CV
authors: Dolan
authors: Psychological Methods, Department of Psychology, University of Amsterdam, Weesperplein 4, 1018 XA, Amsterdam, The Netherlands.
authors: Paul
authors: P
authors: de Boeck
keywords: graded response model; heteroscedasticity; non-normality; normal distribution; skew-normal distribution