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 purpose of the present investigation is to examine the influence of sample size (N) and model complexity on a set of 23 goodness-of-fit (GOF) indices, including those typically used in confirmatory factor analysis. The focus was on two potential problems in assessing GOF: (1) some fit indices are substantially influenced by N so that tests of…

First- and second-round commentaries on an article by L. Guttman are presented. The following authors responded, with two articles each: (1) E. E. Roskam and J. Ellis; (2) P. H. Schonemann; (3) A. R. Jensen; (4) J. C. Loehlin; and (5) J.-E. Gustafsson. (SLD)

The overidentification of structural equation models with latent variables is discussed. The use of two- and three-indicator models is not recommended since such models do not allow a testing of the crucial assumption of unidimensionality among indicators in most cases. Models with four or more indicators may be more sensitive to departures from…

This investigation tested the ability of an a priori hierarchical structure of self-concept derived from the Shavelson model to explain responses to the Self Description Questionnaire (SDQ) III, and demonstrated the application and problems with the use of hierarchical confirmatory factor analysis (HCFA). (Author/JAZ)

This paper provides an up-to-date review of the relationship between item response theory (IRT) and (nonlinear) common factor theory and draws out of this relationship some implications for current and future research in IRT. Nonlinear common factor analysis yields a natural embodiment of the weak principle of local independence in appropriate…

Argues that Jensen's article contains an inaccurate and misleading account of Spearman's work and distorts the basic concepts of factor analysis. The target article has failed in all its main objectives; its major failing is a result of the irrelevance of factor analysis to the study of group differences. (SLD)

The general goal of this paper is to help researchers conduct appropriately designed goodness of fit studies for item response model applications. The specific purposes are to describe: (1) an up-to-date set of promising and useful methods for addressing a variety of goodness of fit questions; and (2) current research studies to advance this set…

Newman (1984) examined the causal relations between math self-concept and math achievement in an 8-year longitudinal study using Linear Structural Relations (LISREL) analyses. He concluded that math self-concept did not influence subsequent math achievement. However, the study suffered in that math self-concept was inferred from a single-item…

The advantages of applying confirmatory factor analysis (CFA) to multitrait-multimethod (MTMM) data are widely recognized. However, because CFA as traditionally applied to MTMM data incorporates single indicators of each scale (i.e., each trait/method combination), important weaknesses are the failure to: (1) correct appropriately for measurement…

The paper identifies and addresses four methodological weaknesses common to most previous studies that have used LISREL confirmatory factor analysis to test for the factorial validity and invariance of a single measuring instrument. Specifically, the paper demonstrates the steps involved in: (1) conducting sensitivity analyses to determine a…