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Mixtures of Conditional Mean- and Covariance-Structure Models

Published online by Cambridge University Press:  01 January 2025

Gerhard Arminger ,
Petra Stein  and
Jörg Wittenberg
Gerhard Arminger*
Affiliation:
Department of Economics, Bergische Universität
Petra Stein
Affiliation:
Department of Social Sciences, Gerhard Mercator Universität
Jörg Wittenberg
Affiliation:
Department of Economics, Bergische Universität
*
Requests for reprints should be sent to Gerhard Arminger, Department of Economics, Bergische Universität, FB6, D-42097 Wuppertal, GERMANY.
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Abstract

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. We discuss the construction of the likelihood function, estimation of the mixture model with regressors using three different EM algorithms, estimation of the asymptotic covariance matrix of parameters and testing for the number of mixture components. In addition to simulation studies, data on food preferences are analyzed.

Keywords

conditional mean- and covariance-structure modelsconditional multivariate normalsEM-algorithmfinite mixturesLISRELminimum-distance-estimation
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 4 , December 1999 , pp. 475 - 494
Copyright
Copyright © 1999 The Psychometric Society

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Footnotes

The authors are grateful to Donald B. Rubin and Michael E. Sobel for critical reading of a first draft of this paper and to three anonymous reviewers of Psychometrika for their helpful comments and suggestions. The research of the first and the third author was supported by a grant from the Deutsche Forschungsgemeinschaft.

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