Covariance structure model when the factor means and the covariances are functions of the third variable

HARUHIKO OGASAWARA

doi:10.4992/psycholres1954.32.19

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Keywords: structured means, factor means, covariance structure analysis, maximum likelihood factor analysis, Fisher's scoring method, multivariate regression analysis

JOURNAL FREE ACCESS

1990 Volume 32 Issue 1 Pages 19-25

DOI https://doi.org/10.4992/psycholres1954.32.19

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Published: February 26, 1990 Received: October 14, 1988 Available on J-STAGE: February 24, 2009 Accepted: July 15, 1989 Advance online publication: - Revised: -
Correction information
Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Akaike, H. 1987 Factor analysis and AIC. Psychometrika, 52, 317-332.
Jöreskog, K. G. 1970 A general method for analysis of covariance structures. Biometrika, 57, 239-251.
Jöreskog, K. G. 1971 Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.
Jöreskog, K. G., & Sörbom, D. 1984 LISREL VI User's guide. Mooresville; Scientific Software Inc.
Lee, S. Y., & Jennrich, R. I. 1979 A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psycfwmetrika, 44, 99-113.
Ogasawara, H. 1986 Maximum likelihood estimation of criteria for age adjustment in intelligence test. Railway Labor Science, 40, 37-53. (In Japanese with English abstract)
Ogasawara, H. 1988 Factor analysis in continuously changing populations. Proceedings of the 16th annual meeting of the Behaviormetric Society of Japan, 85-86. (In Japanese)
Ogasawara, H. 1989 Covariance structure analysis of continuously changing populations. Behaviorrnetrika, 25, 15-33.
Sörbom, D. 1974 A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 27, 229-239.
Sörbom, D. 1981 Structural equation models with structured means. In K. G. Jöreskog & H. Weld (Eds.), Systems under indirect observation: Causality, structure and prediction. Amsterdam: North-Holland. Pp. 183-195.

Right : Akaike, H. 1987 Factor analysis and AIC. Psychometrika, 52, 317-332.
Jöreskog, K. G. 1970 A general method for analysis of covariance structures. Biometrika, 57, 239-251.
Jöreskog, K. G. 1971 Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.
Jöreskog, K. G., &Sörbom, D. 1984 LISREL VI User's guide. Mooresville; Scientific Software Inc.
Lee, S. Y., &Jennrich, R. I. 1979 A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psychometrika, 44, 99-113.
Ogasawara, H. 1986 Maximum likelihood estimation of criteria for age adjustment in intelligence test. Railway Labor Science, 40, 37-53. (In Japanese with English abstract)
Ogasawara, H. 1988 Factor analysis in continuously changing populations. Proceedings of the 16th annual meeting of the Behaviormetric Society of Japan, 85-86.(In Japanese)
Ogasawara, H. 1989 Covariance structure analysis of continuously changing populations. Behaviormetrika, 25, 15-33.
Sörbom, D. 1974 A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 27, 229-239.
Sörbom, D. 1981 Structural equation models with structured means. In K. G. Jöreskog&H. Wold (Eds.), Systems under indirect observation: Causality, structure and prediction. Amsterdam: North-Holland. Pp.183-195.

Date of correction: February 24, 2009 Reason for correction: - Correction: PDF FILE Details: -

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Akaike, H. 1987 Factor analysis and AIC. Psychometrika, 52, 317-332.
Jöreskog, K. G. 1970 A general method for analysis of covariance structures. Biometrika, 57, 239-251.
Jöreskog, K. G. 1971 Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.
Jöreskog, K. G., &Sörbom, D. 1984 LISREL VI User's guide. Mooresville; Scientific Software Inc.
Lee, S. Y., &Jennrich, R. I. 1979 A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psychometrika, 44, 99-113.
Ogasawara, H. 1986 Maximum likelihood estimation of criteria for age adjustment in intelligence test. Railway Labor Science, 40, 37-53. (In Japanese with English abstract)
Ogasawara, H. 1988 Factor analysis in continuously changing populations. Proceedings of the 16th annual meeting of the Behaviormetric Society of Japan, 85-86.(In Japanese)
Ogasawara, H. 1989 Covariance structure analysis of continuously changing populations. Behaviormetrika, 25, 15-33.
Sörbom, D. 1974 A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 27, 229-239.
Sörbom, D. 1981 Structural equation models with structured means. In K. G. Jöreskog&H. Wold (Eds.), Systems under indirect observation: Causality, structure and prediction. Amsterdam: North-Holland. Pp.183-195.

Right : Akaike, H. 1987 Factor analysis and AIC. Psychometrika, 52, 317-332.
Jöreskog, K. G. 1970 A general method for analysis of covariance structures. Biometrika, 57, 239-251.
Jöreskog, K. G. 1971 Simultaneous factor analysis in several populations. Psychometrika, 36, 409-426.
Jöreskog, K. G., & Sörbom, D. 1984 LISREL VI User's guide. Mooresville; Scientific Software Inc.
Lee, S. Y., & Jennrich, R. I. 1979 A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psychometrika, 44, 99-113.
Ogasawara, H. 1986 Maximum likelihood estimation of criteria for age adjustment in intelligence test. Railway Labor Science, 40, 37-53.(In Japanese with English abstract)
Ogasawara, H. 1988 Factor analysis in continuously changing populations. Proceedings of the 16th annual meeting of the Behaviormetric Society of Japan, 85-86.(In Japanese)
Ogasawara, H. 1989 Covariance structure analysis of continuously changing populations. Behaviormetrika, 25, 15-33.
Sörbom, D. 1974 A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 27, 229-239.
Sörbom, D. 1981 Structural equation models with structured means. In K. G. Jöreskog & H. Wold (Eds.), Systems under indirect observation: Causality, structure and prediction. Amsterdam: North-Holland. Pp.183-195.

Abstract

A model in which factor means and factor covariances vary continuously with an external variable is discussed. We assume that, if the covariance matrix of manifest variables should have a certain structure, the means should also have a certain structure characterized by latent variables. In this paper, we discuss two kinds of models. The first is a model in which both means and a covariance matrix of latent variables are functions of an external variable. The second model has structure on the means of manifest variables, but the covariance matrix of the manifest variables is non-structured and constant across the values of the external variable. Finally, the models were fit to the real data in which an external variable “age” was assumed to influence both the means and covariances of the latent variables.

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