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A Taxonomy of Latent Structure Assumptions for Probability Matrix Decomposition Models

Published online by Cambridge University Press:  01 January 2025

Michel Meulders ,
Paul De Boeck  and
Iven Van Mechelen
Michel Meulders*
Affiliation:
Katholieke Universiteit Leuven
Paul De Boeck
Affiliation:
Katholieke Universiteit Leuven
Iven Van Mechelen
Affiliation:
Katholieke Universiteit Leuven
*
Requests for reprints should be sent to Department of Psychology, Tiensestraat 102, B-3000 Leuven, BELGIUM. E-Mail: Michel.Meulders@psy.kuleuven.ac.be
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Abstract

A taxonomy of latent structure assumptions (LSAs) for probability matrix decomposition (PMD) models is proposed which includes the original PMD model (Maris, De Boeck, & Van Mechelen, 1996) as well as a three-way extension of the multiple classification latent class model (Maris, 1999). It is shown that PMD models involving different LSAs are actually restricted latent class models with latent variables that depend on some external variables. For parameter estimation a combined approach is proposed that uses both a mode-finding algorithm (EM) and a sampling-based approach (Gibbs sampling). A simulation study is conducted to investigate the extent to which information criteria, specific model checks, and checks for global goodness of fit may help to specify the basic assumptions of the different PMD models. Finally, an application is described with models involving different latent structure assumptions for data on hostile behavior in frustrating situations.

Keywords

discrete datamatrix decompositionBayesian analysisdata augmentationposterior predictive checkpsychometrics
Type
Articles
Information
Psychometrika , Volume 68 , Issue 1 , March 2003 , pp. 61 - 77
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

Note: The research reported in this paper was partially supported by the Fund for Scientific Research-Flanders (Belgium) (project G.0207.97 awarded to Paul De Boeck and Iven Van Mechelen), and the Research Fund of K.U. Leuven (F/96/6 fellowship to Andrew Gelman, OT/96/10 project awarded to Iven Van Mechelen and GOA/2000/02 awarded to Paul De Boeck and Iven Van Mechelen). We thank Marcel Croon and Kristof Vansteelandt for commenting on an earlier draft of this paper.

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