Abstract
This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.
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References
Aitchison, J. & Silvey, S. D. Maximum likelihood estimation of parameters subject to restraints.Annals of Mathematical Statistics, 1958,29, 813–828.
Anderson, T. W.An introduction to multivariate statistical analysis. New York: Wiley, 1958.
Bertsekas, D. P. Multiplier method: A survey.Automatica, 1976,12, 133–145.
Browne, M. W. Generalized least square estimators in the analysis of covariance structure.South African Statistical Journal, 1975,8, 1–24.
Fletcher, R. & Reeves, C. M. Function minimization by conjugate gradients.Computer Journal, 1964,7, 149–154.
Graybill, F. A.An introduction to linear statistical models. Vol. I. New York: McGraw-Hill, 1961.
Jöreskog, K. G. Simultaneous factor analysis in several populations.Psychometrika, 1971,4, 409–426.
Lee, S. Y. Estimation of covariance structure models with parameters subject to functional restraints.Psychometrika, 1980,45, 309–324, a.
Lee, S. Y. The multiplier method in constrained estimation of covariance structure models.Journal of Statistical Computation and Simulation, 1981,12, 247–257.
Lee, S. Y. & Bentler, P. M. Some asymptotic properties of constrained generalized least squares estimation in covariance structure models.South African Statistical Journal, 1980,14, 121–136.
Lee, S. Y. & Jennrich, R. I. A study of algorithms for covariance structure analysis with specific comparisons using factor analysis.Psychometrika, 1979,43, 99–113.
McDonald, R. P. A simple comprehensive model for the analysis of covariance structures: Some remarks or applications.British Journal of Mathematical and Statistical Psychology, 1980,33, 161–183.
Silvey, D. S. The Lagrangian multiplier test.Annals of Mathematical Statistics, 1959,30, 389–407.
Sörbom, D. & Jöreskog, K. C.COFAMM: confirmatory factor analysis with model modification. Chicago: National Educational Resources, 1976.
Sörbom, D. A general method for studying difference in factor means and factor structure between groups.British Journal of Mathematical and Statistical Psychology, 1974,27, 229–239.
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Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong. The authors are indebted to several anonymous reviewers for suggestions for improvement of this paper.
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Lee, SY., Tsui, KL. Covariance structure analysis in several populations. Psychometrika 47, 297–308 (1982). https://doi.org/10.1007/BF02294161
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DOI: https://doi.org/10.1007/BF02294161