Exploratory factor analysis (EFA) is a commonly used statistical technique for examining the relationships between variables (e.g., items) and the factors (e.g., latent traits) they depict. There are several decisions that must be made when using EFA, with one of the more important being choice of the rotation criterion. This selection can be…

A cross-validation method is described for selecting the significant components from a principal components analysis, and properties of the method are discussed. Parallels are drawn with other related methods in covariance structure modeling, and some comparisons among methods are illustrated with two data sets previously analyzed. (SLD)

Some problems of multiple-group factor rotation based on the parallel proportional profiles and confactor rotation of R. B. Cattell are described, and several alternative modeling solutions are proposed. Benefits and limitations of the structural-modeling approach to oblique confactor resolution are examined, and opportunities for research are…

An iterative process is proposed for obtaining an orthogonal simple structure solution. At each iteration, a target matrix is constructed such that the relative contributions of the target majorize the original ones, factor by factor. The convergence of the procedure is proven, and the algorithm is illustrated. (SLD)

H. F. Kaiser, S. Hunka, and J. Bianchini have presented a method (1971) to compare two matrices of factor loadings based on the same variables, but different groups of individuals. The optimal rotation involved is examined from a mathematical point of view, and the method is shown to be invalid. (SLD)

The issue of indeterminacy in factor analysis and the debate between the proposed alternative solution and posterior moment position are explored in an article and 14 commentaries and rebuttals in two rounds. Implications for applied work involving factor analysis are discussed. (SLD)

An alternative to the PROMAX exploratory method is presented for constructing a target matrix in Procrustean rotation in factor analysis. A technique is proposed based on vector majorization. The approach is illustrated with several standard numerical examples. (SLD)

Enriching factor rotation algorithms with the capacity to conduct repeated searches from random starting points can make the tendency to converge to optima that are merely local a way to catch rotations of the input factors that might otherwise elude discovery. Use of the HYBALL computer program is discussed. (SLD)

Two theorems are presented that describe the conditions under which intercept differences can exist under factorial invariance. In such cases, intercept differences do not result from measurement bias in either the tests or the criterion. The conditions of the theorems are testable, and the test procedures are illustrated. (SLD)

Twelve articles (including two rounds of commentary) consider the proposition that the use of multi-item scales requires only that conditions of simple structure and metric invariance be satisfied at the scale level, rather than for each item individually. The place of the approach in confirmatory factor analysis is debated. (SLD)

The fundamental problems that ipsative measures impose for factor analysis are shown analytically. Normative and ipsative correlation matrices are used to show that the factor pattern induced by ipsativity will overwhelm any factor structure seen with normative factor analysis, making factor analysis not interpretable. (SLD)

An alternative strategy for computing factor scores was introduced and compared to a popular scoring procedure. The new strategy, which involves unit-weighted composites of standardized items with salient factor score coefficients, is shown superior to the common method. Implications of findings are discussed. (SLD)

Used simulation to study the problem of missing item responses in tests and questionnaires when factor analysis is used to study the structure of the items. Factor loadings based on the EM algorithm best approximated the loading structure, with imputation of the mean per person across the scores for that person being the best alternative. (SLD)

The factor analysis of ordered-categorical measures has been described in the literature on factor analysis, but the extension of the analysis to the multiple-population case is less well-known. For example, a comprehensive statement of identification conditions for the multiplepopulation case seems absent in the literature. We review this…

Confirmatory factor analysis evaluated three a priori latent variable models of responses to the Need for Uniqueness Scale completed by 552 undergraduates. An oblique three-factor model best accounted for item commonality. Additional analysis suggests a model with loadings on four modestly correlated factors to explain the scale's latent…