The determination of factors in linear models of factor analysis

Petr Kratochvíl

Aplikace matematiky (1990)

  • Volume: 35, Issue: 5, page 350-355
  • ISSN: 0862-7940

Abstract

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The author shows that a decomposition of a covariance matrix ∑ = 𝐀𝐀 ' implies the corresponding model, i.e. the existence of factors f j such that ∑ a i j 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.

How to cite

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Kratochvíl, Petr. "The determination of factors in linear models of factor analysis." Aplikace matematiky 35.5 (1990): 350-355. <http://eudml.org/doc/15635>.

@article{Kratochvíl1990,
abstract = {The author shows that a decomposition of a covariance matrix $\mathbf \{\sum = AA^\{\prime \}\}$ 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.},
author = {Kratochvíl, Petr},
journal = {Aplikace matematiky},
keywords = {factor score; linear model; existence of factors; singular value decomposition; decomposition of a covariance matrix; singular value decomposition; decomposition of a covariance matrix; existence of factors; general linear model of factor analysis; factor score},
language = {eng},
number = {5},
pages = {350-355},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The determination of factors in linear models of factor analysis},
url = {http://eudml.org/doc/15635},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Kratochvíl, Petr
TI - The determination of factors in linear models of factor analysis
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 5
SP - 350
EP - 355
AB - The author shows that a decomposition of a covariance matrix $\mathbf {\sum = AA^{\prime }}$ 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.
LA - eng
KW - factor score; linear model; existence of factors; singular value decomposition; decomposition of a covariance matrix; singular value decomposition; decomposition of a covariance matrix; existence of factors; general linear model of factor analysis; factor score
UR - http://eudml.org/doc/15635
ER -

References

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  1. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Second Edition, John Wiley & sons, 1984. (1984) Zbl0651.62041MR0771294
  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. (1956) MR0084943
  3. P. Blahuš, Factor analysis and its generalization, Matematický seminář SNTL, sv. 21, Praha 1985 (in Czech, russian translation to appear). (1985) 
  4. P. Kratochvíl J. Nekola, Modelling of the research activity with the use of factor analysis, (Czech). Ekonomicko-matematický obzor 15 (1979), 295-309. (1979) 

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