Numerous methods exist to determine the optimal number of classes when using latent profile analysis (LPA), but none are consistently correct. Recently, the likelihood incremental percentage per parameter (LI3P) was proposed as a model effect-size measure. To evaluate the LI3P more thoroughly, we simulated 50,000 datasets, manipulating factors…

Multidimensional measuring instruments are often used in behavioral, social, educational, marketing, and biomedical research. For these scales, the paper discusses how to find the optimal score based on their components that is associated with the highest possible reliability. Within the framework of structural equation modeling, an approach to…

Simulation studies are needed to investigate how many score categories are sufficient to treat ordered categorical data as continuous, particularly for bifactor models. The current simulation study aims to address such needs by investigating the performance of estimation methods in the bifactor models with ordered categorical data. Results support…

Dynamic structural equation models (DSEM) are designed for time series analysis of latent structures. Inherent to the application of DSEM is model parameter estimation, which has to be addressed in many applications by a single time series. In this context, however, the methods currently available either lack estimation quality or are…

We present a method for Bayesian structural equation modeling of sample correlation matrices as correlation structures. The method transforms the sample correlation matrix to an unbounded vector using the matrix logarithm function. Bayesian inference about the unbounded vector is performed assuming a multivariate-normal likelihood, with a mean…

This study simplifies the seven different cross-lagged panel models (CLPMs) by using the RSEM model for both inter-individual and intra-individual structures. In addition, the study incorporates the newly developed dynamic panel model (DPM), general cross-lagged model (GCLM) and the random intercept auto-regressive moving average (RI-ARMA) model.…

The multiple imputation two-stage (MI2S) approach holds promise for evaluating the model fit of structural equation models for ordinal variables with multiply imputed data. However, previous studies only examined the performance of MI2S-based residual-based test statistics. This study extends previous research by examining the performance of two…

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…

Model evaluation is a crucial step in SEM, consisting of two broad areas: global and local fit, where local fit indices are use to modify the original model. In the modification process, the modification index (MI) and the standardized expected parameter change (SEPC) are used to select the parameters that can be added to improve the fit. The…

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…

Intensive longitudinal data has been widely used to examine reciprocal or causal relations between variables. However, these variables may not be temporally aligned. This study examined the consequences and solutions of the problem of temporal misalignment in intensive longitudinal data based on dynamic structural equation models. First the impact…

This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…

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…

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…