Anomalies in the Allen and Hubbard parallel analysis procedure

Abstract

Allen and Hubbard (1986) increased the accessibility of parallel analysis for principal components applications by developing an equation to predict mean eigenvalues of random data matrices with unities in the diagonals. Two recent studies have shown, however, that Allen and Hubbard’s procedure may yield degenerate solutions-that is, solutions in which succeeding eigenvalues are larger than preceding eigenvalues. The parameters of sample size and number of variables within which the Allen and Hubbard equation degenerates are documented. Implications for the use of this procedure are discussed. Index terms: exploratory factor analysis, factor extraction, parallel analysis, principal components analysis, rules for factor retention.