The use of Lagrange multiplier (LM) tests in specification searches and the efforts that involve the addition of extraneous parameters to models are discussed. Presented are a rationale and strategy for conducting specification searches in two stages that involve adding parameters to LM tests to maximize fit and then deleting parameters not needed…

Different sets of uniqueness constraints may lead to different fit results when applied to the same data in confirmatory factor analysis. Provides several examples of this phenomenon in simulated data and describes reasons for the variation in fit results. Discusses the choice of uniqueness constraints under these circumstances. (SLD)

Discusses a method, based on bootstrap methodology, for obtaining an approximate confidence interval for the difference in root mean square error of approximation of two structural equation models. Illustrates the method using a numerical example. (SLD)

Compared different models suggested for the analysis of multitrait multimethod (MTMM) experiments for their fit to 87 data sets collected in the United States. The fit of models based on polychoric correlations is much worse than the fit of models based on product moment correlations, but in both cases a model that assumes additive method effects…

Examined 20 goodness-of-fit indexes based on the minimum fit function using a simulation under the 2-group situation. Results support the use of the delta comparative fit index, delta Gamma hat, and delta McDonald's Noncentrality Index to evaluation measurement invariance. These three approaches are independent of model complexity and sample size.…

Discusses the difference in noncentrality parameters of nested structural equation models and their utility in evaluating statistical power associated with the pertinent restriction test. Asymptotic confidence intervals for that difference are presented. These intervals represent a useful adjunct to goodness-of-fit indexes in assessing constraints…

Extends the LISREL model to incorporate fixed covariates at both the measurement and the structural equations of the model, establishing a Bayesian procedure with conjugate type prior distributions. Illustrates the efficiency of the algorithm and presents a goodness of fit statistic for assessing the proposed model. (SLD)

Derives approximations to the distributions of goodness-of-fit indexes in structural equation modeling with the assumption of multivariate normality and slight misspecification of models. Also derives an approximation to the asymptotic covariance matrix for the fit indexes by using the delta method and develops approximations to the densities of…

Points out two concerns with recent research by F. Li and others (2000) and T. Duncan and others (1999) that extended the structural equation model of latent interactions developed by K. Joreskog and F. Yang (1996) to latent growth modeling. Used mathematical derivation and a comparison of alternative models fitted to simulated data to develop a…

The relation among fit indexes, power, and sample size in structural equation modeling is examined. The noncentrality parameter is required to compute power. The 2 existing methods of computing power have estimated the noncentrality parameter by specifying an alternative hypothesis or alternative fit. These methods cannot be implemented easily and…

An alternative baseline model for comparative fit assessment of structural equation models is described, evaluated, and compared to the standard "null" baseline model. The new "equal correlation" model constrains all variables to have equal, rather than zero, correlations, but all variances are free. Advantages and limitations…

Discusses concerns with the model proposed by E. Rigdon for computing incremental fit indices in which all measured variables are equally correlated (as opposed to the traditional null model). Proposes retaining the traditional null model with emphasis on the comparative fit of alternative models within a nested sequence that could include the new…

Used three approaches to understand the effect of the number of variables in the model on model fit in structural equation modeling through computer simulation. Developed a simple formula for the theoretical value of the comparative fit index. (SLD)

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…

Used simulation to study the effects of the practice of item parceling. Results indicate that certain types of item parceling can obfuscate a multidimensional factor structure in a way that acceptable values of fit indexes are found for a misspecified solution. Discusses why the use of parceling cannot be recommended when items are…