Simple Versus Complex Factor Analyses of Responses to Multiple Scale Questionnaires

Some effects of using inappropriate criteria for sufficiency of factors are discussed, and examples from the literature used to show how procedures leading to the rotation of large numbers of factors may result in fragmentation and difficulty in interpretation. Analyses of two psychometrically equivalent matrices containing an imposed scale structure led to dissimilar solutions, neither of them revealing the imposed structure, when a minimum eigenvalue of 1.00 was used as a criterion for sufficiency of factors. More conservative (two and three-factor) solutions revealed the imposed scale structure in both matrices. Comparisons with higher-order solutions showed considerable similarity between two-factor solutions and between three-factor solutions at different levels. These contrasted with substantial dissimilarities found in equivalent four-factor solutions. Though the main purpose of the paper is to outline procedures which might reasonably reduce factor fragmentation with its consequent problems of replication and interpretability, the implications of the alternative problem of Underfactoring are also briefly discussed and some solutions suggested.