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…

In factorial survey designs, respondents evaluate multiple short descriptions of social objects (vignettes) that experimentally vary different levels of attributes of interest. Analytical methods (including individual-level regression analysis and multilevel models) estimate the weights (or utilities) assigned to the levels of the different…

Research in human development often relies on composites, that is, composed variables such as indices. Their composite nature renders these variables inaccessible to conventional factor-centric psychometric validation techniques such as confirmatory factor analysis (CFA). In the context of human development research, there is currently no…

To evaluate multidimensional factor structure, a popular method that combines features of confirmatory and exploratory factor analysis is Bayesian structural equation modeling with small-variance normal priors (BSEM-N). This simulation study evaluated BSEM-N as a variable selection and parameter estimation tool in factor analysis with sparse…

Researchers often study dynamic processes of latent variables in everyday life, such as the interplay of positive and negative affect over time. An intuitive approach is to first estimate the measurement model of the latent variables, then compute factor scores, and finally use these factor scores as observed scores in vector autoregressive…

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…

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…

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of…

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…

Self-assessment and reflective thinking (RT) can arm learners to monitor and evaluate their learning progress. Despite the long history of the core of self-assessment (CSA) and RT, little is known about how they may contribute to learner enjoyment (LE) and learner immunity (LI). Therefore, the current research attempted to propose a model to…

When item scores are ordered categorical, categorical omega can be computed based on the parameter estimates from a factor analysis model using frequentist estimators such as diagonally weighted least squares. When the sample size is relatively small and thresholds are different across items, using diagonally weighted least squares can yield a…

We present factor extension procedures for confirmatory factor analysis that provide estimates of the relations of common and unique factors with external variables that do not undergo factor analysis. We present identification strategies that build upon restrictions of the pattern of correlations between unique factors and external variables. The…

During the last 25 years researchers have proposed a number of conceptual frameworks to measure the various functions of instructional leadership. One of the most frequently used frameworks is the Principal Instructional Management Rating Scale (PIMRS). Despite the great number of studies employing the PIMRS, evidence for its reliability and…

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

Using Monte Carlo simulations, this research examined the performance of four missing data methods in SEM under different multivariate distributional conditions. The effects of four independent variables (sample size, missing proportion, distribution shape, and factor loading magnitude) were investigated on six outcome variables: convergence rate,…