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.
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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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Meulders, M., De Boeck, P. & Van Mechelen, I. A taxonomy of latent structure assumptions for probability matrix decomposition models. Psychometrika 68, 61–77 (2003). https://doi.org/10.1007/BF02296653
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DOI: https://doi.org/10.1007/BF02296653