Measurement invariance (MI) is an essential part of validity evidence concerned with ensuring that tests function similarly across groups, contexts, and time. Most evaluations of MI involve multigroup confirmatory factor analyses (MGCFA) that assume simple structure. However, recent research has shown that constraining non-target indicators to…

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…

Measurement invariance holds when a latent construct is measured in the same way across different levels of background variables (continuous or categorical) while controlling for the true value of that construct. Using Monte Carlo simulation, this paper compares the multiple indicators, multiple causes (MIMIC) model and MIMIC-interaction to a…

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…

In exploratory or unrestricted factor analysis, all factor loadings are free to be estimated. In oblique solutions, the correlations between common factors are free to be estimated as well. The purpose of this article is to show how likelihood-based confidence intervals can be obtained for rotated factor loadings and factor correlations, by…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

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 relations among several alternative parameterizations of the binary factor analysis model and the 2-parameter item response theory model are discussed. It is pointed out that different parameterizations of factor analysis model parameters can be transformed into item response model theory parameters, and general formulas are provided.…

A simulation study was conducted to examine the effect of item parceling on confirmatory factor analysis parameter estimates and their standard errors at different levels of sample size, number of indicators per factor, size of factor structure/pattern coefficients, magnitude of interfactor correlations, and variations in item-level data…

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,…