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…

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

Yuan and Hayashi (2010) introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS…

In this article, a 2-way multigroup common factor model (MG-CFM) is presented. The MG-CFM can be used to estimate interaction effects between 2 grouping variables on 1 or more hypothesized latent variables. For testing the significance of such interactions, a likelihood ratio test is presented. In a simulation study, the robustness of the…

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 paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package "rsem" to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables…

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust…

A Monte Carlo simulation was conducted to investigate the robustness of 4 latent variable interaction modeling approaches (Constrained Product Indicator [CPI], Generalized Appended Product Indicator [GAPI], Unconstrained Product Indicator [UPI], and Latent Moderated Structural Equations [LMS]) under high degrees of nonnormality of the observed…