A frequent criticism of exploratory factor analysis (EFA) is that it does not allow correlated residuals to be modelled, while they can be routinely specified in the confirmatory (CFA) model. In this article, we propose an EFA approach in which both the common factor solution and the residual matrix are unrestricted (i.e., the correlated residuals…

This simulation study investigated the sensitivity of commonly used cutoff values for global-model-fit indexes, with regard to different degrees of violations of the assumption of uncorrelated errors in confirmatory factor analysis. It is shown that the global-model-fit indexes fell short in identifying weak to strong model misspecifications under…

This article shows how interfactor correlation is affected by error correlations. Theoretical and practical justifications for error correlations are given, and a new equivalence class of models is presented to explain the relationship between interfactor correlation and error correlations. The class allows simple, parsimonious modeling of error…

Both ad-hoc robust sandwich standard error estimators (design-based approach) and multilevel analysis (model-based approach) are commonly used for analyzing complex survey data with nonindependent observations. Although these 2 approaches perform equally well on analyzing complex survey data with equal between- and within-level model structures…

In 1959, Campbell and Fiske introduced the use of multitrait-multimethod (MTMM) matrices in psychology, and for the past 4 decades confirmatory factor analysis (CFA) has commonly been used to analyze MTMM data. However, researchers do not always fit CFA models when MTMM data are available; when CFA modeling is used, multiple models are available…

Ordinal variables are common in many empirical investigations in the social and behavioral sciences. Researchers often apply the maximum likelihood method to fit structural equation models to ordinal data. This assumes that the observed measures have normal distributions, which is not the case when the variables are ordinal. A better approach is…

The Rosenberg Self-Esteem scale (RSE) has been widely used in examinations of sex differences in global self-esteem. However, previous examinations of sex differences have not accounted for method effects associated with item wording, which have consistently been reported by researchers using the RSE. Accordingly, this study examined the…

This article examines 4 approaches for explaining shared method variance, each applied to a longitudinal trait-state-occasion (TSO) model. Many approaches have been developed to account for shared method variance in multitrait-multimethod (MTMM) data. Some of these MTMM approaches (correlated method, orthogonal method, correlated method minus one,…

In this investigation, we used a classic latent profile analysis (LPA), a person-centered approach, to identify groups of students who had similar profiles for multiple dimensions of academic self-concept (ASC) and related these LPA groups to a diverse set of correlates. Consistent with a priori predictions, we identified 5 LPA groups representing…

The recovery of weak factors has been extensively studied in the context of exploratory factor analysis. This article presents the results of a Monte Carlo simulation study of recovery of weak factor loadings in confirmatory factor analysis under conditions of estimation method (maximum likelihood vs. unweighted least squares), sample size,…

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, as when individuals are randomly drawn from groups that are randomly drawn from a target population. When the covariance structures in the group level and the individual level are the…