# Article

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Keywords:
factor score; linear model; existence of factors; singular value decomposition; decomposition of a covariance matrix
Summary:
The author shows that a decomposition of a covariance matrix $\bold{\sum = AA'}$ implies the corresponding model, i.e. the existence of factors $f_j$ such that $\sum a_{ij}f_j$ is true. The result is applied to the general linear model of factor analysis. A procedure for computing the factor score is proposed.
References:
[1] T. W. Anderson: An Introduction to Multivariate Statistical Analysis. Second Edition, John Wiley & sons, 1984. MR 0771294 | Zbl 0651.62041
[2] T. W Anderson, Herman Rubin: Statistical inference in factor analysis. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (Jerzy Neyman, ed.), Vol. V, University of California, Berkeley and Los Angeles, 1956. MR 0084943
[3] P. Blahuš: Factor analysis and its generalization. Matematický seminář SNTL, sv. 21, Praha 1985 (in Czech, russian translation to appear).
[4] P. Kratochvíl J. Nekola: Modelling of the research activity with the use of factor analysis. (Czech). Ekonomicko-matematický obzor 15 (1979), 295-309.

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