Matrix decomposition structural equation modeling (MDSEM) is introduced as a novel approach in structural equation modeling, contrasting with traditional structural equation modeling (SEM). MDSEM approximates the data matrix using a model generated by the hypothetical model and addresses limitations faced by conventional SEM procedures by…

Cross-loadings are common in multiple-factor confirmatory factor analysis (CFA) but often ignored in measurement invariance testing. This study examined the impact of ignoring cross-loadings on the sensitivity of fit measures (CFI, RMSEA, SRMR, SRMRu, AIC, BIC, SaBIC, LRT) to measurement noninvariance. The manipulated design factors included the…

When comparing relations and means of latent variables, it is important to establish measurement invariance (MI). Most methods to assess MI are based on confirmatory factor analysis (CFA). Recently, new methods have been developed based on exploratory factor analysis (EFA); most notably, as extensions of multi-group EFA, researchers introduced…

A full structural equation model (SEM) typically consists of both a measurement model (describing relationships between latent variables and observed scale items) and a structural model (describing relationships among latent variables). However, often researchers are primarily interested in testing hypotheses related to the structural model while…

Factor mixture modeling (FMM) is generally complex with both unobserved categorical and unobserved continuous variables. We explore the potential of item parceling to reduce the model complexity of FMM and improve convergence and class enumeration accordingly. To this end, we conduct Monte Carlo simulations with three types of data, continuous,…

Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: [sigma] = [sigma(theta)] when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS…

In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…

When a covariance structure model is misspecified, parameter estimates will be affected. It is important to know which estimates are systematically affected and which are not. The approach of analyzing the path is both intuitive and informative for such a purpose. Different from path analysis, analyzing the path uses path tracing and elementary…

In the exploratory factor analysis, when the number of factors exceeds the true number of factors, the likelihood ratio test statistic no longer follows the chi-square distribution due to a problem of rank deficiency and nonidentifiability of model parameters. As a result, decisions regarding the number of factors may be incorrect. Several…

Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are…

In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an…

The overarching intent of this article is to exemplify strategies associated with tests for measurement invariance that are uncommonly applied and reported in the extant literature. Designed within a pedagogical framework, the primary purposes are 3-fold and illustrate (a) tests for measurement invariance based on the analysis of means and…

This article is concerned with the seemingly simple problem of testing whether latent factors are perfectly correlated (i.e., statistically indistinct). In recent literature, researchers have used different approaches, which are not always correct or complete. We discuss the parameter constraints required to obtain such perfectly correlated latent…

This is the first study to test whether the stages of change of the transtheoretical model are qualitatively different through exploring discontinuity patterns in theory of planned behavior (TPB) variables using latent multigroup structural equation modeling (MSEM) with AMOS. Discontinuity patterns in terms of latent means and prediction patterns…

This study focused on misspecifications in composing parcels to represent a latent construct. Two measurement design factors, item reliability and intercorrelations among parcels, defined 12 true unidimensional parcel models. Deviations from the true model were examined via a 2-facet measurement model in which items and parcels represented the 2…