Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…

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…

Because research has shown that principals' practices can significantly impact teaching and learning in their schools through multiple avenues, it is critical to understand the validity of tools that measure principal practice. While the field has relied heavily on self-report surveys, little is known about their validity. This study compares…

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…

A test for linear trend among a set of eigenvalues of a correlation matrix is described. It is a generalization of G. Anderson's (1965) test for the equality of eigenvalues and extends the present authors' previous work on linear trends in eigenvalues of a covariance matrix. The linear trend hypothesis is discussed. (SLD)

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)

Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)

Higher order factor analysis is an extension of factor analysis that is little used, but which offers the potential to model the hierarchical order often seen in natural (including psychological) phenomena more accurately. The process of higher order factor analysis is reviewed briefly, and various interpretive aids, including the Schmid-Leiman…

Demonstrates that traditional exploratory factor analytic methods, when applied to correlation matrices, cannot be used to estimate unattenuated factor loadings. Presents a mathematical basis for the accurate estimation of such values when the disattenuated correlation matrix or the covariance matrix is used as input. Explains how the equations…

The difference in statistical power between the original Bonferroni and five modified Bonferroni procedures that control the overall Type I error rate is examined in the context of a correlation matrix where multiple null hypotheses are tested. Power differences of less than 0.05 were typically observed for the modified Bonferroni procedures. (SLD)

The general factor of mental ability ("g") may reflect general biological fitness. If so, "g"-loaded measures such as Raven's progressive matrices should be related to morphological measures of fitness such as fluctuating asymmetry (FA: left-right asymmetry of a set of typically left-right symmetrical body traits such as finger…

Some suggestions for measuring marginal symmetry in agreement matrices for categorical data are discussed, together with measures of item-by-item agreement conditional on marginal asymmetry. Connections with intraclass correlations for dichotomous data are noted. (Author)

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution that need not be centered row-wise. The results bear directly on several types of preprocessing methods in Parafac/Candecomp. (Author/TJH)

The originally proposed multivariate meta-analysis approach for correlation matrices--analyze Pearson correlations, with each study's observed correlations replacing their population counterparts in its conditional-covariance matrix--performs poorly. Two refinements are considered: Analyze Fisher Z-transformed correlations, and substitute better…