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…

An extension of multiple correspondence analysis is proposed that takes into account cluster-level heterogeneity in respondents' preferences/choices. The method involves combining multiple correspondence analysis and k-means in a unified framework. The former is used for uncovering a low-dimensional space of multivariate categorical variables…

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…

Taxicab correspondence analysis is based on the taxicab singular value decomposition of a contingency table, and it shares some similar properties with correspondence analysis. It is more robust than the ordinary correspondence analysis, because it gives uniform weights to all the points. The visual map constructed by taxicab correspondence…

Three approaches to the analysis of main and interaction effect hypotheses in nonorthogonal designs were compared in a 2 x 2 design for data that was neither normal in form nor equal in variance. The Welch-James test with trimmed means and Winsorized variances provided excellent Type I error control. (SLD)

Explores the robustness of conclusions from a statistical model against variations in model choice with an illustration from G. Box and G. Tiao (1973). Suggests that simultaneous consideration of a class of models for the same data is sometimes superior to analyzing the data under one model and demonstrates advantages to Adaptive Bayesian…

The percentage bend correlation coefficient is introduced as one way to address the problem that the usual correlation coefficient is highly nonrobust. While this method is not a replacement for the usual test, it can offer advantages in terms of power and Type I errors. (SLD)

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)

Examined the asymptotic distributions of three reliability coefficient estimates: (1) sample coefficient alpha; (2) reliability estimate of a composite score following factor analysis; and (3) maximal reliability of a linear combination of item scores after factor analysis. Findings show that normal theory based asymptotic distributions for these…

A theoretical framework is developed in which the effects of some common forms of violation of assumptions of linearity of regression and homoscedasticity can be investigated. Simple expressions are derived for the restricted and corrected correlations in terms of the target (unrestricted) correlation in these situations. (SLD)

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. Majorization is used at several stages in the minimization procedure to obtain a monotonically convergent algorithm. A simulation study and empirical data illustrate the procedure. (SLD)

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)

Two estimators of effect size that are based on the sample quartiles are proposed and studied. One is for the situation where a treatment effect is evaluated against a control group, and the other is for a situation in which two parallel treatments are compared. Both are illustrated and evaluated. (SLD)

This paper explains how to obtain generally robust and powerful analyses with any of the recommended nonorthogonal solutions by adapting a modification of the Welch-James procedure for comparing means when population variances are heterogeneous. Results from a Monte Carlo study support use of the procedure. (SLD)

Using Monte Carlo methods, the applicability of large sample theory to maximum likelihood estimates of total indirect effects in sample sizes of 50, 100, 200, 400, and 800 was studied. Samples of at least 200 and 400 are required for the recursive and nonrecursive models, respectively, that were assessed. (TJH)