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Estimating Multiple Classification Latent Class Models

Published online by Cambridge University Press:  01 January 2025

E. Maris
E. Maris*
Affiliation:
Department of Mathematical Psychology, Nijmegen Institute for Cognition and Information (NICI) National Institute for Educational Measurement (CITO)
*
Requests for reprints should be sent to Eric Maris, Vakgroep Mathematische Psychologie K.U. Nijmegen, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Abstract

This paper presents a new class of models for persons-by-items data. The essential new feature of this class is the representation of the persons: every person is represented by its membership to multiple latent classes, each of which belongs to one latent classification. The models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number of mental operations. Two algorithms for maximum likelihood (ML) and maximum a posteriori (MAP) estimation are described. They both make use of the tractability of the complete data likelihood to maximize the observed data likelihood. Properties of the MAP estimators (i.e., uniqueness and goodness-of-recovery) and the existence of asymptotic standard errors were examined in a simulation study. Then, one of these models is applied to the responses to a set of fraction addition problems. Finally, the models are compared to some related models in the literature.

Keywords

latent class modelslatent response modelscognitive processesEM-algorithm
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 2 , June 1999 , pp. 187 - 212
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

Thanks are to Paul De Boeck for creating the intellectually stimulating atmosphere in which this class of models came about, Iven van Mechelen for the one-sided idea, Kikumi Tatsuoka for the use of her data, and Theodoor Bouw for running part of the simulation study.

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