CEFA 3.02(Browne, Cudeck, Tateneni, & Mels, 2008) is a factor analysis computer program designed to perform exploratory factor analysis. It provides the main properties that are needed for exploratory factor analysis, namely a variety of factoring methods employing eight different discrepancy functions to be minimized to yield initial…

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)

Various analytic choices in principal components and common factor analysis are discussed. Differences and similarities among these extraction methods are explained, and aids in interpreting the origin of detected effects are explored. Specifically, the nature and use of structure and pattern coefficients are examined. Communalities and methods…

A relatively simple technique for assessing the convergence of sets of variables across method domains is presented. The technique, two-step principal components analysis, empirically orthogonalizes each method domain into sets of components, and then analyzes convergence among components across domains. (Author)

Five techniques that combine the ideals of rotation of matrices of factor loadings to optimal agreement and rotation to simple structure are compared on the basis of empirical and contrived data. Combining a generalized Procrustes analysis with Varimax on the main of the matched loading matrices performed well on all criteria. (SLD)

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)

Nonlinear factor analysis is a tool commonly used by measurement specialists to identify both the presence and nature of multidimensionality in a set of test items, an important issue given that standard Item Response Theory models assume a unidimensional latent structure. Results from most factor-analytic algorithms include loading matrices,…

Procedures for analyzing common item effects on interscale structure were reviewed and a study using smallest space analysis of the California Psychological Inventory (CPI) reported. Solutions of three matrices--intercorrelation matrix of the original CPI scales, of reduced scales (with common items removed), and of the number of common…

The cognitive structure of an algebra test was defined and validated using the linear test model (LLTM) and quadratic assignment (QA) techniques. The LLTM is an extension of the Rasch model with a linear constraint that describes item difficulty in terms of the cognitive operations required to solve the item. The model permits the specification of…