, Volume 21, Issue 3, pp 273–285 | Cite as

“Best possible” systematic estimates of communalities

  • Louis Guttman


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.


Public Policy Statistical Theory Variable Increase Systematic Estimate Minimum Rank 
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Copyright information

© Psychometric Society 1956

Authors and Affiliations

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

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