Mediation analysis is an important statistical tool in many research fields, where the joint significance test is widely utilized for examining mediation effects. Nevertheless, the limitation of this mediation testing method stems from its conservative Type I error, which reduces its statistical power and imposes certain constraints on its…

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…

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…

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…

Adapts robust schemes to mean and covariance structures, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is weighted according to its distance, based on first and second order moments. Test statistics and standard error estimators are given. (SLD)

Assessed the robustness of an estimation method for multilevel and path analysis with hierarchical data proposed by B. Muthen (1989) with unequal groups and small sample sizes and in the presence of a low or high intraclass correlation. Simulation results show the effects of varying these conditions on the within-group and between-groups part of…

The sensitivity analysis of structural equation models when minor perturbation is introduced is investigated. An influence measure based on the general case weight perturbation is derived for the generalized least squares estimation, and an influence measure is developed for the special case deletion perturbation scheme. (Author/SLD)

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…

Formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the Wishart maximum likelihood estimation for normally and nonnormally distributed variables. When multivariate normality is satisfied, considerable simplification is obtained for the models of unstandardized variables. Formulas…

A Monte Carlo study explores the robustness assumption in structural equation modeling of using a full information normal theory generalized least-squares estimation procedure on Type I censored data. The efficacy of the following proposed alternate estimation procedures is assessed: asymptotically distribution free estimator and a latent…

At grades 8 and 12, the 1992 National Assessment of Educational Progress (NAEP) reading assessment contained a small number of 50-minute blocks in addition to the usual 25-minute blocks. To determine whether to incorporate the 50-minute blocks into the operational scaling, this study sought to determine whether the longer blocks measured a…