The meta-analysis of factor analyses: An illustration based on the cumulation of correlation matrices.

Abstract

This article introduces and illustrates a procedure for aggregating data from several factor analyses in a meta-analysis. The central idea is to combine the correlation matrices first and then perform a new factor analysis. Special attention is given to the handling of general factors in data sets and to the use of correlations corrected for attenuation. Bushman, Cooper, and Lemke (1991) recently introduced a procedure for comparing factor loadings derived in two samples of subjects. When there are more than two samples, the procedure is repeated for all possible pairs of samples. Essentially, the method determines the level of congruence between corresponding factors and requires knowledge only of the factor matrix, which, as the authors pointed out, is one of its major attractions. However, although Bushman el al.'s (1991) use of a method for determining congruence among factors has its merits, ordinarily only zero-order correlations can legitimately be cumulated across studies (Hunter & Schmidt. 1990, pp. 503-504). Furthermore, the congruence method, following Thompson's (1989) criteria for determining whether a study should be included in such comparisons, requires that, in the results being compared, the same variables and no additional variables appear, the same extraction method be used, and the same transformation or rotation method be followed. When correlations are aggregated, however, these requirements, as well as the additional requirement that the same number of factors be extracted, are irrelevant.

A confirmatory factor analysis of the beck depression inventory-II in end-stage renal disease patients

“…Given that the measurement of depression symptoms is complex when applied to chronically ill patients, validation of screening tools is paramount. As suggested by others [19,39] the G-S-C may well be a suitable model from which validation studies can be based. The G-S-C decomposes cognitive and somatic factors from general depression symptoms, thus potentially allowing criterion relationships to be defined against diagnostic standards for depression, and also with antecedent factors.…”

Meta-analysis of the factor structures of four depression questionnaires: Beck, CES-D, Hamilton, and Zung

“…Two potential drawbacks of using confirmatory factor analysis for meta-analysis are that it requires specification in advance of the model to be tested, which may be unknown or unclear in areas utilizing exploratory factor analyses, and it requires that the original covariance matrices for the samples be tested. Becker (1996) presents a method for the meta-analysis of factor analysis that is based on accumulating the original correlation matrices across studies. Once meta-analytic estimates of an aggregated correlation matrix have been computed, a single factor analysis can be conducted.…”

Parameter accuracy in meta‐analyses of factor structures

“…After aggregating the k reproduced correlation matrices , the pooled correlation matrix is subjected to a conventional exploratory factor analysis that yields as an estimate of Λ . Thus, the indirect approach can be conceived as an extension of Becker's () two‐step strategy, albeit based on the reproduced instead of the sample correlation matrices. Although both approaches achieve the same goal of providing an estimate of Λ , the indirect approach is more flexible because it does not assume a priori knowledge of a specific factor configuration and, thus, could even be used to aggregate loading patterns with a different number of factors.…”