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

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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.