Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

According to Kenny and McCoach (2003), chi-square tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range of 48 to 960 degrees of freedom it was found that…

Effects of incomplete data on fit indexes remain relatively unexplored. We evaluate a wide set of fit indexes (?[squared], root mean squared error of appproximation, Normed Fit Index [NFI], Tucker-Lewis Index, comparative fit index, gamma-hat, and McDonald's Centrality Index) varying conditions of sample size (100-1,000 in increments of 50),…

Conventional wisdom in missing data research dictates adding variables to the missing data model when those variables are predictive of (a) missingness and (b) the variables containing missingness. However, it has recently been shown that adding variables that are correlated with variables containing missingness, whether or not they are related to…

Structural equation modeling allows several methods of estimating the disattenuated association between 2 or more latent variables (i.e., the measurement model). In one common approach, measurement models are specified using item parcels as indicators of latent constructs. Item parcels versus original items are often used as indicators in these…

The overarching intent of this article is to exemplify strategies associated with tests for measurement invariance that are uncommonly applied and reported in the extant literature. Designed within a pedagogical framework, the primary purposes are 3-fold and illustrate (a) tests for measurement invariance based on the analysis of means and…

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…

To date, finite mixtures of structural equation models (SEMMs) have been developed and applied almost exclusively for the purpose of providing model-based cluster analyses. This type of analysis constitutes a direct application of the model wherein the estimated component distributions of the latent classes are thought to represent the…

A covariance structure modeling method to test equality in proportions explained variance in studied unobserved dimensions by means of latent predictors is outlined. The procedure is applicable with multiple-indicator, structural equation models where of interest is to compare the predictive power of sets of latent independent variables for given…

A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

The purpose of this study was to evaluate the robustness of estimated growth curve models when there is stationary autocorrelation among manifest variable errors. The results suggest that when, in practice, growth curve models are fitted to longitudinal data, alternative rival hypotheses to consider would include growth models that also specify…

A method for estimation of reliability for multiple-component measuring instruments with clustered data is outlined. The approach is applicable with hierarchical designs where individuals are nested within higher order units and exhibit possibly related performance on components of a scale of interest. The procedure is developed within the…

This study examines the growth and development of structural equation modeling (SEM) from the years 1994 to 2001. The synchronous development and growth of the Structural Equation Modeling journal was also examined. Abstracts located on PsycINFO were used as the primary source of data. The major results of this investigation were clear: (a) The…

This study examined the measurement and latent construct invariance of the Academic Motivation Scale (Vallerand, Blais, Brier, & Pelletier, 1989; Vallerand et al., 1992, 1993) across both gender and time. An integrative analytical strategy was used to assess in one set of nested models both longitudinal and cross-gender invariance, and…

We consider power calculation in structural equation modeling with data missing completely at random (MCAR). Muth?n and Muth?n (2002) recently demonstrated how power calculations with data MCAR can be carried out by means of a Monte Carlo study. Here we show that the method of Satorra and Saris (1985), which is based on the nonnull distribution of…