Despite the sensitivity of fit indices to various model and data characteristics in structural equation modeling, these fit indices are used in a rigid binary fashion as a mere rule of thumb threshold value in a search for model adequacy. Here, we address the behavior and interpretation of the popular Comparative Fit Index (CFI) by stressing that…

American Educational Research Association (AERA) standards stipulate that researchers show evidence of the internal structure of instruments. Confirmatory factor analysis (CFA) is one structural equation modeling procedure designed to assess construct validity of assessments that has broad applicability for counselors interested in instrument…

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…

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about…

I-states-as-objects-analysis (ISOA) is a person-oriented methodology for studying short-term developmental stability and change in patterns of variable values. ISOA is based on longitudinal data with the same set of variables measured at all measurement occasions. A key concept is the "i-state," defined as a person's pattern of variable…

Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, "M", and the outcome, "Y". This assumption holds if individuals are randomly…

SEMModComp, a software package for conducting likelihood ratio tests for mean and covariance structure modeling is described. The package is written in R and freely available for download or on request.

Traditional estimators of fit measures based on the noncentral chi-square distribution (root mean square error of approximation [RMSEA], Steiger's [gamma], etc.) tend to overreject acceptable models when the sample size is small. To handle this problem, it is proposed to employ Bartlett's (1950), Yuan's (2005), or Swain's (1975) correction of the…

Outlines a method for comparing completely standardized solutions in multiple groups. The method is based on a correlation structure analysis of equal-size samples and uses the correlation distribution theory implemented in the structural equation modeling program RAMONA. (SLD)

This article illustrates the use of the SAS system for Monte Carlo simulation work in structural equation modeling (SEM). Data generation procedures for both multivariate normal and nonnormal conditions are discussed, and relevant SAS codes for implementing these procedures are presented. A hypothetical example is presented in which Monte Carlo…

Provides select power and sample size tables and interpolation strategies associated with the root mean square error of approximation test of not close fit under standard assumed conditions. The goal is to inform researchers conducting structural equation modeling about power limitations when testing a model. (SLD)

To complement recent articles in this journal on structural equation modeling (SEM) practice and principles by Martens and by Quintana and Maxwell, respectively, the authors offer a consumer's guide to SEM. Using an example derived from theory and research on vocational psychology, the authors outline six steps in SEM: model specification,…

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…

The authors describe 2 efficiency (planned missing data) designs for measurement: the 3-form design and the 2-method measurement design. The 3-form design, a kind of matrix sampling, allows researchers to leverage limited resources to collect data for 33% more survey questions than can be answered by any 1 respondent. Power tables for estimating…

Structural equation modeling (SEM) refers to a family of statistical techniques that explores the relationships among a set of variables. Structural equation modeling provides an extremely versatile method to model very specific hypotheses involving systems of variables, both measured and unmeasured. Researchers can use SEM to study patterns of…