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Fitting and Testing Conditional Multinormal Partial Credit Models

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  • David Hessen

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. Copyright The Psychometric Society 2012

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  • David Hessen, 2012. "Fitting and Testing Conditional Multinormal Partial Credit Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 693-709, October.
    • Handle: RePEc:spr:psycho:v:77:y:2012:i:4:p:693-709
    DOI: 10.1007/s11336-012-9277-1
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    References listed on IDEAS

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    1. Henk Kelderman & Carl Rijkes, 1994. "Loglinear multidimensional IRT models for polytomously scored items," Psychometrika, Springer;The Psychometric Society, vol. 59(2), pages 149-176, June.
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    8. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
    9. Henk Kelderman, 1992. "Computing maximum likelihood estimates of loglinear models from marginal sums with special attention to loglinear item response theory," Psychometrika, Springer;The Psychometric Society, vol. 57(3), pages 437-450, September.
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    Cited by:

    1. David J. Hessen, 2023. "Fitting and Testing Log-Linear Subpopulation Models with Known Support," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 917-939, September.
    2. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    3. Gunter Maris & Timo Bechger & Ernesto Martin, 2015. "A Gibbs Sampler for the (Extended) Marginal Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 859-879, December.
    4. Mia J. K. Kornely & Maria Kateri, 2022. "Asymptotic Posterior Normality of Multivariate Latent Traits in an IRT Model," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1146-1172, September.

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