## Principal factor analysis, Advanced Statistics

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Principal factor analysis is the method of factor analysis which is basically equivalent to a principal components analysis performed on reduced covariance matrix attained by replacing the diagonal elements of the sample variance-covariance matrix with the estimated communalities.

The two often used estimates of the latter are
(a) the square of the multiple correlation coefficient of ith variable with all the other variables,
(b) the largest of the absolute values of the correlation coefficients between the ith variable and one of other variables

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