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Computing the Standards Errors of Mixture Model Parameters with EM when Classes are Well Separated

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  • Michel Wedel

    (University of Groningen
    The University of Michigan Business School)

Abstract

Summary It is shown that for finite mixtures the missing information tends to zero as the number of observations on each subject increases. Then, the classes become perfectly separated (i.e. the posterior membership probabilities are close to 0 or 1), the observed information tends to the complete information and the class-specific parameters in the mixture model become information orthogonal across classes. Then the asymptotic standard errors of parameter estimates can be obtained directly from the EM algorithm. The degree of class-separation is derived for which the amount of missing observation is approximately negligible and the asymptotic standard errors based on the complete information matrix are sufficiently accurate. Empirical illustrations are provided. A Monte Carlo study is performed to examine the extent to which the approximation is adequate. A comparison is made with other methods to approximate the observed information matrix. It is concluded that if the entropy of the posterior probabilities is larger than 0.95 the proposed approximation is reasonably accurate.

Suggested Citation

  • Michel Wedel, 2001. "Computing the Standards Errors of Mixture Model Parameters with EM when Classes are Well Separated," Computational Statistics, Springer, vol. 16(4), pages 539-558, December.
    • Handle: RePEc:spr:compst:v:16:y:2001:i:4:d:10.1007_s180-001-8329-3
    DOI: 10.1007/s180-001-8329-3
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    References listed on IDEAS

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    1. Wedel, Michel & DeSarbo, Wayne S, 1996. "An Exponential-Family Multidimensional Scaling Mixture Methodology," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 447-459, October.
    2. Conor Dolan & Han Maas, 1998. "Fitting multivariage normal finite mixtures subject to structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 227-253, September.
    3. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    4. 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.
    5. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
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