The purpose of this article is to describe the analytic process of a method of data collection known as Q Methodology. This method is an alternative method in collecting data especially suited to research on "points of views" (Coogan & Herrington, 2011, p. 24). The analytic process of Q methodology involves factor analysis, a…

The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

Many researchers recognize that factor analysis can be conducted on both correlation matrices and variance-covariance matrices. Although most researchers extract factors from non-distribution free or parametric methods, researchers can also extract factors from distribution free or non-parametric methods. The nature of the data dictates the method…

Exploratory factor analysis involves five key decisions. The second decision, how many factors to retain, is the focus of the current paper. Extracting too many or too few factors often leads to devastating effects on study results. The advantages and disadvantages of the most effective and/or most utilized strategies to determine the number of…

Researchers often argue that the structural models of the constructs they study are relevant to clinicians. Unfortunately, few clinicians are able to translate the mathematically precise relationships between latent constructs and observed scores into information that can be usefully applied to individuals. Typically this means that when a new…

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…

This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…

The purpose of this study was to investigate the application of the parallel analysis (PA) method for choosing the number of factors in component analysis for situations in which data are dichotomous or ordinal. Although polychoric correlations are sometimes used as input for component analyses, the random data matrices generated for use in PA…

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

Influence curves of some parameters under various methods of factor analysis depend on the influence curves for either the covariance or the correlation matrix used in the analysis. The differences between the two types of curves are derived, and simple formulas for the differences are presented. (SLD)

Many people believe that environmental factors promote giftedness and invest in many programs to adopt gifted students providing them with challenging activities. Intellectual giftedness is founded on fluid intelligence and extends to more specific abilities through the growth and inputs from the environment. Acknowledging the roles played by the…

A full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion is provided. Matrix differential calculus is used in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented. (Author/JKS)

Procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix so that it becomes optimally simple. How the Harris and Kaiser independent cluster (1964) rotation can be modified to obtain a simple weights matrix rather than a simple pattern is described and illustrated. (SLD)

Gives sufficient and necessary conditions for the observability of factors in terms of the parameter matrices and a finite number of variables. Outlines five conditions that rigorously define indeterminacy and shows that (un)observable factors are (in)determinate, and extends L. Guttman's (1955) proof of indeterminacy to Heywood (H. Heywood, 1931)…

Provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally the approach relies on repeated orthomax rotation applied to supermatrices containing the frontal, lateral, or horizontal slabs, respectively. Exemplary analyses illustrate the procedure. (Author/SLD)