Abstract
We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix σ under the usual factor analysis model. For suitable choices ofj, λ j (σ), where λ j (σ) is thej-th largest eigenvalue of σ, provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - λ p (σ) improves on the use of squared mulitiple correlation coefficient as a lower bound.
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This research was done while the second author was at Tokyo Institute of Technology.
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Yanai, H., Ichikawa, M. New lower and upper bounds for communality in factor analysis. Psychometrika 55, 405–409 (1990). https://doi.org/10.1007/BF02295295
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DOI: https://doi.org/10.1007/BF02295295