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Pseudo Maximum Likelihood Estimation and a Test for Misspecification in Mean and Covariance Structure Models

Published online by Cambridge University Press:  01 January 2025

Gerhard Arminger  and
Ronald J. Schoenberg
Gerhard Arminger
Affiliation:
Bergische Universität Wuppertal
Ronald J. Schoenberg*
Affiliation:
Aptech Systems
*
Requests for reprints should be sent to Ronald Schoenberg, Aptech Systems, 26250-196th Place S.E., Kent, WA 98042.
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Abstract

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.

Keywords

covariance structure analysisEQSHausman testLISRELKullback Leibler information criterionmisspecificationomitted variable biaspseudo and quasi-maximum likelihood estimation

Information

Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 409 - 425
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.

References

Aptech Systems (1989). GAUSS 2.0 user's guide, Kent, WA: Author.Google Scholar
Bentler, P. M. (1985). Theory and implementation of EQS, a structural equations program, Los Angeles: BMDP Statistical Software.Google Scholar
Browne, M. W. (1974). Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 8, 1–24.Google Scholar
Browne, M. W. (1984). Asymptotic distribution-free methods for the analysis of covariance structures. British Journal of Mathematical & Statistical Psychology, 37, 62–83.CrossRefGoogle ScholarPubMed
Gourieroux, C., Monfort, A., & Trognon, A. (1984). Pseudo maximum likelihood methods: Theory. Econometrica, 52, 681–700.CrossRefGoogle Scholar
Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46, 1251–1272.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. (1986). LISREL user's guide, Mooresville: Scientific Software.Google Scholar
Rao, C. R. (1973). Linear statistical inference and its applications, New York: Wiley.CrossRefGoogle Scholar
Satorra, A. (1989). Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika, 54, 131–151.CrossRefGoogle Scholar
Satorra, A., & Bentler, P. M. (1987). Robustness properties of ML statistics in covariance structure analysis. Unpublished manuscript. University of California at Los Angeles.Google Scholar
Schoenberg, R. J. (1989). LINCS: Linear covariance structure analysis. User's guide, Kent, WA: RJS Software.Google Scholar
Shapiro, A. (1986). Asymptotic theory of overparameterized structural models. Journal of the American Statistical Association, 81, 142–149.CrossRefGoogle Scholar
White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48, 817–838.CrossRefGoogle Scholar
White, H. (1981). Consequences and detection of misspecified nonlinear regression models. Journal of the American Statistical Association, 76, 419–433.CrossRefGoogle Scholar
White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50, 1–25.CrossRefGoogle Scholar