This article discusses replication sampling variance estimation techniques that are often applied in analyses using data from complex sampling designs: jackknife repeated replication, balanced repeated replication, and bootstrapping. These techniques are used with traditional analyses such as regression, but are currently not used with structural…

Relevant aspects of the example provided by Raykov and Marcoulides (2001) are emphasized, specifically the distinctiveness of infinitely many members of its sequence of equivalent structural equation models. This emphasis appears to be needed in light of recent statements by Markus (2002), whose intended counterexamples do not present a…

Four methods for estimating a dynamic factor model, the direct autoregressive factor score (DAFS) model, are evaluated and compared. The first method estimates the DAFS model using a Kalman filter algorithm based on its state space model representation. The second one employs the maximum likelihood estimation method based on the construction of a…

In research concerning model invariance across populations, researchers have discussed the limitations of the conventional chi-square difference test ([Delta] chi-square test). There have been some research efforts in using goodness-of-fit indexes (i.e., [Delta]goodness-of-fit indexes) for assessing multisample model invariance, and some specific…

Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor…

The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were…

The latent state-trait (LST) theory is an extension of the classical test theory that allows one to decompose a test score into a true trait, a true state residual, and an error component. For practical applications, the variances of these latent variables may be estimated with standard methods of structural equation modeling (SEM). These…

A readily implemented procedure is discussed for interval estimation of indexes of interrelationship between items from multiple-component measuring instruments as well as between items and total composite scores. The method is applicable with categorical (ordinal) observed variables, and can be widely used in the process of scale construction,…

This article examines 4 approaches for explaining shared method variance, each applied to a longitudinal trait-state-occasion (TSO) model. Many approaches have been developed to account for shared method variance in multitrait-multimethod (MTMM) data. Some of these MTMM approaches (correlated method, orthogonal method, correlated method minus one,…

Structural equation modeling provides the framework for investigating experimental effects on the basis of variances and covariances in repeated measurements. A special type of confirmatory factor analysis as part of this framework enables the appropriate representation of the experimental effect and the separation of experimental and…

Recent missing data studies have argued in favor of an "inclusive analytic strategy" that incorporates auxiliary variables into the estimation routine, and Graham (2003) outlined methods for incorporating auxiliary variables into structural equation analyses. In practice, the auxiliary variables often have missing values, so it is reasonable to…

The relations among several alternative parameterizations of the binary factor analysis model and the 2-parameter item response theory model are discussed. It is pointed out that different parameterizations of factor analysis model parameters can be transformed into item response model theory parameters, and general formulas are provided.…

The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the…

This article presents a didactic discussion of a multilevel covariance structure modeling approach to estimation of lowest level mediation effect indexes in two-level studies. The procedure is useful when addressing questions about relations among total and indirect effects between variables of interest while accounting for the hierarchical…

In social science research, an indirect effect occurs when the influence of an antecedent variable on the effect variable is mediated by an intervening variable. To compare indirect effects within a sample or across different samples, structural equation modeling (SEM) can be used if the computer program supports model fitting with nonlinear…