Factor Comparability As A Means Of Determining The Number Of Factors And Their Rotation

Abstract

Several methods, mostly based on a consideration of the eigenvalues, have been previously used to determine the number of factors to retain in a factor analysis. This paper shows how split-half factor comparabilities, based on factor scores, can provide a direct and unambiguous method of determining the number of reliable factors that should be retained, and of assessing the appropriate rotation that should be used. The method is particularly appropriate for taxonomic factor analysis, where the factor scores are to be used as summary or classificatory measures. It is shown that, for respondents from non-homogenous populations, split-halves based on the sub-populations should be considered, as well as random split-halves. The discussion is supported by a number of principal components analyses, using synthetic data sets of known factor structure and an actual semantic response data bank.

Personality development from 12 to 18 years of age: changes in mean levels and structure of traits

“…Coefficients of congruence for five factors with the adult structure are presented in Table 2. All but one (Openness in the 6th grade) were above 0.90, which is typically regarded as a threshold for replication (Everett, 1983). The mean congruence coefficient (see the last column in Table 2) increased from 0.87 in the 6th grade to 0.94, 0.96, and 0.96 in the 8th, 10th, and 12th grades, respectively.…”

Tracking the hypersensitive dimension in narcissism: Reliability and validity of the Hypersensitive Narcissism Scale

“…Starting from these considerations and following McRae and colleagues ' (1996) suggestions, we assessed the correct number of factors to be extracted from the polychoric correlation matrices using three different methods, namely Everett's (1983) factor comparability method, quasi-inferential parallel analysis (Buja and Eyuboglu, 1992) and the scree plot. Principal component analysis was used to decompose the HSNS item correlation matrix.…”

The Biographical Inventory in Naval Aviation Selection: Inside the Black Box

“…Each method was applied to the 56-item intercorrelation matrices for two random halves of the sample to assess the replicability of their results in view of the instability of factor analyses of items (Gorsuch, 1974). The methods were: (a) a scree test of eigenvalues based on a principal-axis factor analysis with squared multiple correlations as communality estimates (Cattell, 1966); (b) parallel analysis of random data for a principal-axis factor analysis with squared multiple correlations as communality estimates (Montanelli & Humphreys, 1976); (c) consistent salient loadings in the two halves for principal-axis factor analyses with squared multiple correlations as communality estimates and Varimax (Kaiser, 1958) rotations, the analyses done for varying numbers of factors (Carroll, 1985); and (d) comparability coefficients based on factor scores (computed by the multipleregression method) for principal-axis factor analyses with iterated communality estimates and Varimax and Promax rotations (Hendrickson & White, 1964) for the two halves, the factor analyses done for varying numbers of factors (Everett, 1983).…”