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An Extended Model Comparison Framework for Covariance and Mean Structure Models, Accommodating Multiple Groups and Latent Mixtures

Author

Listed:
  • Roy Levy

    (Arizona State University, Tempe, AZ, USA, roy.levy@asu.edu)

  • Gregory R. Hancock

    (University of Maryland, College Park, MD, USA)

Abstract

The model comparison framework of Levy and Hancock for covariance and mean structure models is extended to treat multiple-group models, both in cases in which group membership is known and in those in which it is unknown (i.e., finite mixtures). The framework addresses questions of distinguishability as well as difference in fit of the models with respect to data, first by determining the nature of the models’ relation in terms of the families of distributions that constitute the models and then by conducting the appropriate statistical tests. In the case of latent mixtures of groups, the standard likelihood ratio theory does not apply, and a bootstrapping approach is used to facilitate the tests. Illustrations demonstrate the procedures.

Suggested Citation

  • Roy Levy & Gregory R. Hancock, 2011. "An Extended Model Comparison Framework for Covariance and Mean Structure Models, Accommodating Multiple Groups and Latent Mixtures," Sociological Methods & Research, , vol. 40(2), pages 256-278, May.
    • Handle: RePEc:sae:somere:v:40:y:2011:i:2:p:256-278
    DOI: 10.1177/0049124111404819
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    References listed on IDEAS

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    1. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-678, May.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    3. G. J. McLachlan, 1987. "On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 318-324, November.
    4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    5. 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.
    6. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    7. Neal O. Jeffries, 2003. "A note on 'Testing the number of components in a normal mixture'," Biometrika, Biometrika Trust, vol. 90(4), pages 991-994, December.
    8. Robert Mislevy & Norman Verhelst, 1990. "Modeling item responses when different subjects employ different solution strategies," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 195-215, June.
    9. Stanley Sclove, 1987. "Application of model-selection criteria to some problems in multivariate analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 333-343, September.
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