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Heteroscedastic Latent Trait Models for Dichotomous Data

Published online by Cambridge University Press:  01 January 2025

Dylan Molenaar
Dylan Molenaar*
Affiliation:
University of Amsterdam
*
Correspondence 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
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Abstract

Effort has been devoted to account for heteroscedasticity with respect to observed or latent moderator variables in item or test scores. For instance, in the multi-group generalized linear latent trait model, it could be tested whether the observed (polychoric) covariance matrix differs across the levels of an observed moderator variable. In the case that heteroscedasticity arises across the latent trait itself, existing models commonly distinguish between heteroscedastic residuals and a skewed trait distribution. These models have valuable applications in intelligence, personality and psychopathology research. However, existing approaches are only limited to continuous and polytomous data, while dichotomous data are common in intelligence and psychopathology research. Therefore, in present paper, a heteroscedastic latent trait model is presented for dichotomous data. The model is studied in a simulation study, and applied to data pertaining alcohol use and cognitive ability.

Keywords

heteroscedasticitylatent trait modelsitem response theorytwo-parameter modelnon-normal latent variables
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 3 , September 2015 , pp. 625 - 644
Copyright
Copyright © 2014 The Psychometric Society

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