Convergence of estimates of unique variances in factor analysis, based on the inverse sample covariance matrix

If the ratio m/p tends to zero, where m is the number of factors m and p the number of observable variables, then the inverse diagonal element of the inverted observable covariance matrix (ςpjj)-1 tends to the corresponding unique variance ψjj for almost all of these (Guttman, 1956). If the smallest singular value of the loadings matrix from Common Factor Analysis tends to infinity as p increases, then m/p tends to zero. The same condition is necessary and sufficient for (ςpjj)-1 to tend to ψjj for all of these. Several related conditions are discussed. (PsycINFO Database Record (c) 2009 APA, all rights reserved) (journal abstract