Image Theory for the Structure of Quantitative Variates  

Oleh:

Guttman, Louis

Jenis: Article from Journal - e-Journal
Dalam koleksi: Psychometrika: A Journal of Quantitative Psychology vol. 18 no. 4 (Dec. 1953), page 277-296.
Topik: Notion o.f "Commonness"; Common-Factor Theory; Observed Correlation Matrix; Inverse of the Correlation Matrix; Least-Squares Images; Determininate Common Factors
Fulltext: Vol 18 No 4 Dec 1953 p.277-296.pdf (1,022.45KB)

Isi artikel

A universe of infinitely many quantitative variables is considered, from which a sample ofn variables is arbitrarily selected. Only linear least-squares regressions are considered, based on an infinitely large population of individuals or respondents. In the sample of variables, the predicted value of a variablex from the remainingn - 1 variables is called the partial image ofx, and the error of prediction is called the partial anti-image ofx. The predicted value ofx from the entire universe, or the limit of its partial images asn ? 8, is called the total image ofx, and the corresponding error is called the total anti-image. Images and anti-images can be used to explain “why” any two variablesx j andx k are correlated with each other, or to reveal the structure of the intercorrelations of the sample and of the universe. It is demonstrated that image theory is related to common-factor theory but has greater generality than common-factor theory, being able to deal with structures other than those describable in a Spearman-Thurstone factor space. A universal computing procedure is suggested, based upon the inverse of the correlation matrix.

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