Matched Determiners Vs. Factor Invariance: A Reply To Korth

Korth (1978) does well to describe factor matching as vital to personality research but seriously underestimates the extent of successful matching both within and between cultures. His evaluation of matching of a set of factors is an advance, but the achievement of "diagonalization" of r[SUBc] coefficients in a matching matrix probably has a higher significance than his method would indicate. Regarding Monte Carlo determinations of r[SUBc] distributions, the writer maintains that treating loadings as random normal deviates is incorrect and that a special distribution (here presented) is required. Further, it is argued that "factor invariance," as commonly defined, is not the required proof of identify of determiners. Instead, the principles of real base factor analysis need to be applied to demonstrate degree of matching of determiners. A numerical illustration shows that when congruence is actually perfect for the real base factor patterns, it is not so for ordinary factor analysis patterns. Even in this framework the congruence, coefficient has weaknesses, and it is suggested that decisions be based on the joint outcome of r[SUBc] and 8, the salient variable similarity index.