Discusses the utility of multilevel confirmatory factor analysis and hierarchical linear modeling methods in testing measurement models in which the underlying attribute may vary as a function of levels of observation. A real dataset is used to illustrate the two approaches and their comparability. (SLD)

By postulating that the random utilities associated with the choice options follow a multivariate normal distribution, Thurstonian models (Thurstone, 1927) provide a straightforward representation of paired comparison data. The use of Monte Carlo Expectation-Maximization (MCEM) algorithms and limited information approaches have been proposed to…

The adequacy of "rule of thumb" conventional cutoff criteria and several alternatives for fit indices in covariance structure analysis was evaluated through simulation. Analyses suggest that, for all recommended fit indexes except one, a cutoff criterion greater than (or sometimes smaller than) the conventional rule of thumb is required…

Improper structures arising from the estimation of parameters in structural equation models (SEMs) are commonly an indication that the model is incorrectly specified. The use of boundary solutions cannot in general be recommended. Partly on the basis of theory given by Van Driel, and partly by example, suggestions are made for using the data as…

In recent years, confirmatory factor analytic (CFA) techniques have become the most common method of testing for measurement equivalence/invariance (ME/I). However, no study has simulated data with known differences to determine how well these CFA techniques perform. This study utilizes data with a variety of known simulated differences in factor…

A widely and readily applicable covariance structure modeling approach is outlined that allows point and interval estimation of scale reliability with fixed components. The procedure employs only linear constraints introduced in a congeneric model, which after reparameterization permit expression of composite reliability as a function of…

In applications of structural equation modeling, it is often desirable to obtain measures of uncertainty for special functions of model parameters. This article provides a didactic discussion of how a method widely used in applied statistics can be employed for approximate standard error and confidence interval evaluation of such functions. The…

In addition to assessing the rate of change in outcome measures, it may be useful to test the significance of outcome changes during specific time periods within an entire observation period under study. While discussing the delta method and bootstrapping, this study demonstrates how to use these 2 methods to estimate the standard errors of the…

Discusses issues related to model evaluation in structural equation modeling. Supports nested model comparisons via sequential chi-square difference tests as consistent with the four-step approach to model evaluation when models of the factor analytic simultaneous equation type are entertained. (Author/SLD)

This article presents a methodology for examining the content and nature of item parcels as indicators of a conceptually defined latent construct. An essential component of this methodology is the 2-facet measurement model, which includes items and parcels as facets of construct indicators. The 2-facet model tests assumptions required for…

We consider the question of how variation in the number and reliability of indicators affects the power to reject the hypothesis that the regression coefficients are zero in latent linear regression analysis. We show that power remains constant as long as the coefficient of determination remains unchanged. Any increase in the number of indicators…

This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results, even in…

This article describes a technique to analyze randomized response data using available structural equation modeling (SEM) software. The randomized response technique was developed to obtain estimates that are more valid when studying sensitive topics. The basic feature of all randomized response methods is that the data are deliberately…

We demonstrate a model for categorical data that parallels the MIMIC model for continuous data. The model is equivalent to a latent class model with observed covariates; further, it includes simple handling of missing data. The model is used on data from a large-scale study of HIV that had both biological measures of infection and self-report…

This article considers the implications for other noncentrality parameter-based statistics from Steiger's (1998) multiple sample adjustment to the root mean square error of approximation (RMSEA) measure. When a structural equation model is fitted simultaneously in more than 1 sample, it is shown that the calculation of the noncentrality parameter…