Assessed the extent to which results in exploratory factor analysis (EFA) studies can be replicated by confirmatory factor analysis in the same sample. Used 10 factor structures drawn from the literature. Results show that confirmatory factor models in which all low EFA pattern coefficients were fixed to zero fitted especially poorly. (SLD)

The factor structure of the "KeyMath--Revised Normative Update" (KMR-NU) "Form A" was analyzed using data from a sample of 130 students. The KMR-NU is composed of 13 subtests that are purported to measure three important aspects of math ability: Basic Concepts, Operations, and Applications. A confirmatory factor analysis…

The Schmid-Leiman (J. Schmid and J. M. Leiman, 1957) decomposition of a hierarchical factor model converts the model to a constrained case of a bifactor model with orthogonal common factors that is equivalent to the hierarchical model. This article discusses the equivalence of the hierarchical and bifactor models. (Author/SLD)

Demonstrated that the extra-factor phenomenon (the two-dimensional solution produced when linear factor analysis is applied to a set of unfoldable items) arises because the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model and the unidimensional quadratic factor model is not distinguishable from the…

In the technique developed by K. G. Joreskog to solve the problem for oblique rotation to a specified simple structure, the basic concept is that the simple structure solution itself is determined only by the zero coefficients of the reference-structure matrix and not by the coefficients of non-zero magnitude. Following this, prior information…

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)

The purpose of this study is to determine the latent structure of the California Verbal Learning Test-Second Edition (CVLT-II; Delis, Kramer, Kaplan, & Ober, 2000) at three different age levels, using the standardization sample. Maximum likelihood confirmatory factor analyses are performed to test four competing hypothetical models for fit and…

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…

The partial correlation coefficient is derived analytically under exemplary factor patterns. In these patterns, variables are described as an additive composition of a set of orthogonal factors, including general, common, and specific factors. Viewed in this framework, it is evident that the partial correlation may yield spurious results.…

The use of the 2 x 2 matrix in qualitative data analysis and theory generation is discussed, embracing the perspective that the objective of qualitative research in general and the analysis of qualitative data in particular is the development of theory. A 2 x 2 matrix is considered to be a tabular representation of the relationship of two…

Generalizations of L. A. Goodman's RC(M) association model (1991 and earlier) are presented for three-way tables. These three-mode association models use L. R. Tucker's three-mode components model (1964, 1966) to represent the three-factor interaction or the combined effects of two- and three-factor interactions. (SLD)

Multidimensional scaling (MDS) and exploratory and confirmatory factor analyses were compared in the assessment of the dimensionality of data sets, using sets generated to be one-dimensional or two-dimensional and differing in degree of interdimensional correlation and number of items defining a dimension. (SLD)

The representation of multivariate data by icons is discussed. The factorial sun is suggested as superior to the commonly used snowflake or sun icons and as better representing the values of the different variables and their correlational structure. Two experiments with 60 college students demonstrate the factorial sun's superiority. (SLD)

A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the…

Use of parallel analysis (PA), a selection rule for the number-of-factors problem, is investigated from the viewpoint of permutation assessment through a Monte Carlo simulation. Results reveal advantages and limitations of PA. Tables of sample eigenvalues are included. (SLD)