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…

When a researcher proposes an SEM model to explain the dynamics among some latent variables, the real question in model evaluation is the fit of the model's structural part. A composite index that lumps the fit of the structural part and measurement part does not directly address that question. The need for more attention to structural-level fit…

We propose new ways of robustifying goodness-of-fit tests for structural equation modeling under non-normality. These test statistics have limit distributions characterized by eigenvalues whose estimates are highly unstable and biased in known directions. To take this into account, we design model-based trend predictions to approximate the…

We extended current knowledge by examining the performance of several Bayesian model fit and comparison indices through a simulation study using the confirmatory factor analysis. Our goal was to determine whether commonly implemented Bayesian indices can detect specification errors. Specifically, we wanted to uncover any differences in detecting…

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…

Despite the popularity of traditional fit index cutoffs like RMSEA [less than or equal to] 0.06 and CFI [greater than or equal to] 0.95, several studies have noted issues with overgeneralizing traditional cutoffs. Computational methods have been proposed to avoid overgeneralization by deriving cutoffs specifically tailored to the characteristics…

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…

Hybrid autoregressive-latent growth structural equation models for longitudinal data represent a synthesis of the autoregressive and latent growth modeling frameworks. Although these models are conceptually powerful, in practice they may struggle to separate autoregressive and growth-related processes during estimation. This confounding of change…

The present study was motivated by the theory-method mismatch between heterotypic continuity (aspects of development that manifest differently across the lifespan thus cannot be measured the same way over time) and longitudinal measurement equivalence (the statistical assumption that the developmental phenomenon studied is measured on the same…

Nonnormality of data presents unique challenges for researchers who wish to carry out structural equation modeling. The subsequent SPSS syntax program computes bootstrap-adjusted fit indices (comparative fit index, Tucker-Lewis index, incremental fit index, and root mean square error of approximation) that adjust for nonnormality, along with the…

Our purpose was to examine different approaches to modeling the time-varying nature of exceptionality classification. Using longitudinal data from one state's mathematics achievement test for 28,829 students in Grades 3 to 8, we describe the reclassification rate within special education and between general and special education, and compare four…

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test…

The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have…

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen's (Psychometrika 61:109-121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator…

Conducted a meta-analysis focusing on the explanation of empirical Type I error rates for six principal classes of estimators. Generally, chi-square tests for overall model fit were found to be sensitive to nonnormality and the size of the model for all estimators, with the possible exception of elliptical estimators with respect to model size and…