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Finite Mixtures of Covariance Structure Models with Regressors

Author

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  • GERHARD ARMINGER

    (Bergische Universität Wuppertal)

  • PETRA STEIN

    (Mercator Universität Duisburg)

Abstract

Models of finite mixtures of normal densities conditional on regressor variables are specified and estimated. The authors consider mixtures of multivariate normals where the expected value for each component depends on nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. The authors discuss the construction of the likelihood function and outline the estimation of parameters. In addition, they define fit indices and discuss aspects of model specification and modification that are specific to mixtures of mean- and covariance-structures. Finally, they give an empirical example in which they analyze the importance of automobiles to individuals depending on the latent constructs individualism and ecology-mindedness. It is shown that the sample under consideration comes from three heterogeneous subpopulations. It is demonstrated that each subpopulation may be characterized by a different mean- and covariance-structure.

Suggested Citation

  • Gerhard Arminger & Petra Stein, 1997. "Finite Mixtures of Covariance Structure Models with Regressors," Sociological Methods & Research, , vol. 26(2), pages 148-182, November.
    • Handle: RePEc:sae:somere:v:26:y:1997:i:2:p:148-182
    DOI: 10.1177/0049124197026002002
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    References listed on IDEAS

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    1. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    2. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
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