Generalized structured component analysis (GSCA) is a multivariate method for specifying and examining interrelationships between observed variables and components. Despite its data-analytic flexibility honed over the decade, GSCA always defines every component as a linear function of observed variables, which can be less optimal when observed…

Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact…

Path models with observed composites based on multiple items (e.g., mean or sum score of the items) are commonly used to test interaction effects. Under this practice, researchers generally assume that the observed composites are measured without errors. In this study, we reviewed and evaluated two alternative methods within the structural…

In this article, the authors extend the results of Aguirre-Urreta, Rönkkö, and Marakas (2016) concerning the omission of a relevant causal indicator by testing the validity of the assumption that causal indicators are entirely superfluous to the measurement model and discuss the implications for measurement theory. Contrary to common wisdom…

Given that the root mean square error of approximation (RMSEA) is currently one of the most popular measures of goodness-of-model fit within structural equation modeling (SEM), it is important to know how well the RMSEA performs in models with small degrees of freedom ("df"). Unfortunately, most previous work on the RMSEA and its…

Several studies have stressed the importance of simultaneously estimating interaction and quadratic effects in multiple regression analyses, even if theory only suggests an interaction effect should be present. Specifically, past studies suggested that failing to simultaneously include quadratic effects when testing for interaction effects could…

The present study assessed the impact of sample size on the power and fit of structural equation modeling applied to functional brain connectivity hypotheses. The data consisted of time-constrained minimum norm estimates of regional brain activity during performance of a reading task obtained with magnetoencephalography. Power analysis was first…

Statistical analyses investigating latent structure can be divided into those that estimate structural model parameters and those that detect the structural model type. The most basic distinction among structure types is between categorical (discrete) and dimensional (continuous) models. It is a common, and potentially misleading, practice to…

In research concerning model invariance across populations, researchers have discussed the limitations of the conventional chi-square difference test ([Delta] chi-square test). There have been some research efforts in using goodness-of-fit indexes (i.e., [Delta]goodness-of-fit indexes) for assessing multisample model invariance, and some specific…

Examined several hypotheses about the suitability of the noncentral chi square in applied research using Monte Carlo simulation experiments with seven sample sizes and three distinct model types, each with five specifications. Results show that, in general, for models with small to moderate misspecification, the noncentral chi-square is well…

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…