The Contribution of Communality Estimation to the Achievement of Factorial Invariance, With Special Reference to the Mmpi

Abstract

One purpose of communality estimation in factor analysis is to promote factorial invariance, i.e., to improve the chances of recovering demonstrably related factor structures from diverse sets of variables and samples of subjects. Recognition of this purpose may help to resolve ambiguities that have appeared in efforts to define unique communalities for isolated correlation matrices. The estimation of even approximate values for communality may be well worth the effort as a contribution to factorial invariance. A convenient, programable procedure is described that leads simultaneously to useful estimates of communality and of the number of factors. On the basis of actual data for two samples, properties of the communalities obtained by this procedure are compared with those obtained from a conventional principal axis analysis using diagonal entries of unity. The clinical scales of the MMPI, plus Si, are judged to provide reliable measurement on at least eight orthogonal dimensions, each well‐marked by a different scale. Stable differences exist in the item‐reliabilities of the ten scales studied. Neither of these consistencies in the data for the two samples was available from application of the conventional analysis. Tucker's procedure for examining factor congruence is found to be capable of yielding misleading results in the context of poor communality estimates.

A Factor Analysis of the Mathematical Sections of the Scholastic Aptitude Test1

“…This procedure facilitated impressionistic comparisons of factor loadings of Table 7 with those from the analysis of the correlation matrix reported in Table 1, although any strict quantitative comparisons would be inappropriate. Next, communality estimates were obtained by the method described by Saunders (1960) and Wrigley (1956). The first 10 principal axis factors of the modified covariance matrix were extracted.…”

“…Of the remaining 58, all were either specifics or consisted of essentially trivial entries. main diagonal, and (2) a principal-axis factoring of the tetrachoric 'covariance matrix 3 using communality estimates obtained by an iterative procedure first suggested by Wrigley (1956) and later advocated by Saunders (1960). For the first method, the principal-axis factors of s-l(R -S2)S-1 were taken as discussed in Harris (1962)~S2 = (diagR-l)-l~.…”

Evidence Bearing on the Existence of a Rational Correspondence Between the Personality Typologies of Spranger and of Jung

“…Beginning with the covariance matrix obtained from the larger sUb-sample (not reported) and initial communality estimates of' zero for all variables, we employed a familiar procedure (9) to estimate the number of significant factors and the associated final communalities. The data required exactly nine common factors.…”

A factor analysis of the picture completion items of the WAIS

“…Tetrachoric correlations were computed by machine, and are reported in Table 1. The factor analysis was carried out using an iterative procedure for communality estimation (7). Stable results for three factors were obtained after four iterations.…”