“Best Possible” Systematic Estimates of Communalities  

Oleh:

Guttman, Louis

Jenis: Article from Journal - e-Journal
Dalam koleksi: Psychometrika: A Journal of Quantitative Psychology vol. 21 no. 3 (Sep. 1956), page 273-285.
Topik: Systematic Estimates; Determinacy of Unique-Factor Scores; "Best Possible" Estimates; Equality When n Is Finite
Fulltext: Vol 21 No.3 Sept 1956 p.273-285.pdf (667.19KB)

Isi artikel

At least four approaches have been used to estimate communalities that will leave an observed correlation matrixR Gramian and with minimum rank. It has long been known that the square of the observed multiple-correlation coefficient is a lower bound to any communality of a variable ofR. This lower bound actually provides a “best possible” estimate in several senses. Furthermore, under certain conditions basic to the Spearman-Thurstone common-factor theory, the bound must equal the communality in the limit as the number of observed variables increases. Otherwise, this type of theory cannot hold forR.

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