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Psychometrika

, Volume 18, Issue 4, pp 277–296 | Cite as

Image theory for the structure of quantitative variates

  • Louis Guttman
Article

Abstract

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 → ∞, 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.

Keywords

Public Policy Large Population Correlation Matrix Statistical Theory Quantitative Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Psychometric Society 1953

Authors and Affiliations

  • Louis Guttman
    • 1
  1. 1.The Israel Institute of Applied Social ResearchIsrael

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