This note demonstrates that measurement invariance does not guarantee meaningful and valid group comparisons in multiple-population settings. The article follows on a recent critical discussion by Robitzsch and Lüdtke, who argued that measurement invariance was not a pre-requisite for such comparisons. Within the framework of common factor…

Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

Factor Score Regression (FSR) is increasingly employed as an alternative to structural equation modeling (SEM) in small samples. Despite its popularity in psychology, the performance of FSR in multigroup models with small samples remains relatively unknown. The goal of this study was to examine the performance of FSR, namely Croon's correction and…

Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or…

We develop a structural after measurement (SAM) method for structural equation models (SEMs) that accommodates missing data. The results show that the proposed SAM missing data estimator outperforms conventional full information (FI) estimators in terms of convergence, bias, and root-mean-square-error in small-to-moderate samples or large samples…

In educational and psychological research, it is common to use latent factors to represent constructs and then to examine covariate effects on these latent factors. Using empirical data, this study applied three approaches to covariate effects on latent factors: the multiple-indicator multiple-cause (MIMIC) approach, multiple group confirmatory…

Network meta-analysis (NMA) uses both direct and indirect evidence to compare the efficacy and harm between several treatments. Structural equation modeling (SEM) is a statistical method that investigates relations among observed and latent variables. Previous studies have shown that the contrast-based Lu-Ades model for NMA can be implemented in…

Several multivariate models are motivated to answer similar developmental questions regarding within-person (intraindividual) effects between 2 or more constructs over time, yet the within-person effects tested by each model are distinct. In this article, the authors clarify the types of within-person inferences that can be made from each model.…

In the discussion of mean square difference (MSD) and standard error of measurement (SEM), Barchard (2012) concluded that the MSD between 2 sets of test scores is greater than 2(SEM)[superscript 2] and SEM underestimates the score difference between 2 tests when the 2 tests are not parallel. This conclusion has limitations for 2 reasons. First,…

In this study, the authors compared the likelihood ratio test and fit indexes for detection of misspecifications of growth shape in latent growth models through a simulation study and a graphical analysis. They found that the likelihood ratio test, MFI, and root mean square error of approximation performed best for detecting model misspecification…

This study used structural equation modeling to examine the effect of Stratum III (i.e., general intelligence) and Stratum II (i.e., Comprehension-Knowledge, Fluid Reasoning, Short-Term Memory, Processing Speed, and Visual Processing) factors of the Cattell-Horn-Carroll (CHC) cognitive abilities, as operationalized by the Wechsler Intelligence…

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…

This study assessed effectiveness of an educational community intervention taught by "promotoras de salud" in reducing cardiovascular disease (CVD) risk among Hispanics using a structural equation modeling (SEM) approach. Model development was guided by a social ecological framework proposing CVD risk reduction through improvement of…

The question whether a person's attained socioeconomic position is mainly due to hers/his intelligence, socioeconomic background, or level of education, has sparked some controversy. In the present study, the effects of these three variables, as well as emotional capacity, on attained occupational position and on income were analyzed with…

There have been many discussions of how Type I errors should be controlled when many hypotheses are tested (e.g., all possible comparisons of means, correlations, proportions, the coefficients in hierarchical models, etc.). By and large, researchers have adopted familywise (FWER) control, though this practice certainly is not universal. Familywise…