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Fitting and Testing Conditional Multinormal Partial Credit Models

Published online by Cambridge University Press:  01 January 2025

David J. Hessen
David J. Hessen*
Affiliation:
Utrecht University
*
Requests for reprints should be sent to David J. Hessen, Department of Methodology and Statistics, Utrecht University, Heidelberglaan 1, PO Box 80.140, 3508 TC Utrecht, The Netherlands. E-mail: D.J.Hessen@uu.nl
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Abstract

A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in Psychometrika 55:5–18, 1990). In the model, latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item scores, which are sufficient statistics. Attention is paid to maximum likelihood estimation of item parameters, multivariate moments of latent variables, and person parameters. It is shown that the maximum likelihood estimates can be found without the use of numerical integration techniques. More general models are discussed which can be used for testing the model, and it is shown how models with different numbers of latent variables can be tested against each other. In addition, multi-group extensions are proposed, which can be used for testing both measurement invariance and latent population differences. Models and procedures discussed are demonstrated in an empirical data example.

Keywords

partial credit modelmultivariate normal distributionfactor analysismulti-group modelmeasurement invariance

Information

Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012 , pp. 693 - 709
Copyright
Copyright © 2012 The Psychometric Society

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