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Probability Matrix Decomposition Models

Published online by Cambridge University Press:  01 January 2025

Eric Maris ,
Paul De Boeck  and
Iven Van Mechelen
Eric Maris*
Affiliation:
University of Nijmegen
Paul De Boeck
Affiliation:
University of Leuven
Iven Van Mechelen
Affiliation:
University of Leuven
*
Requests for reprints should be sent to Eric Maris, Nijmegen Institute for Cognition and Information, Department of Mathematical Psychology, University of Nijmegen, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS (E-mall: U212776@VM.UCI.KUN.NL).
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Abstract

In this paper, we consider a class of models for two-way matrices with binary entries of 0 and 1. First, we consider Boolean matrix decomposition, conceptualize it as a latent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition models. Second, probability matrix decomposition (PMD) models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models. Third, an algorithm for the computation of the maximum likelihood (ML) and the maximum a posteriori (MAP) estimates of the parameters of PMD models is presented. This algorithm is an EM-algorithm, and is a special case of a more general algorithm that can be used for the whole class of LRMs. And fourth, as an example, a PMD model is applied to data on decision making in psychiatric diagnosis.

Keywords

Boolean matrix decompositionlatent response modelclusteringtwo-way dataincomplete dataEM-algorithmpsychiatric diagnosis

Information

Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 1 , March 1996 , pp. 7 - 29
Copyright
© 1996 The Psychometric Society

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Footnotes

This paper is based on a chapter of the first author's doctoral dissertation, written at the University of Leuven and supervised by Paul De Boeck.

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