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)

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)

Information fit indexes such as Akaike Information Criterion, Consistent Akaike Information Criterion, Bayesian Information Criterion, and the expected cross validation index can be valuable in assessing the relative fit of structural equation models that differ regarding restrictiveness. In cases in which models without mean restrictions (i.e.,…

Continuing a discussion of the topic of fit assessment in structural equation modeling, this article accepts the compromise proposed by H. Marsh (1998) and offers tentative heuristic models for interpreting fit indices that involve the new baseline model proposed by E. Rigdon (1998). (SLD)

Sample covariance matrices constructed with pairwise deletion for randomly missing data were used in a simulation with three sample sizes and five levels of missing data (up to 50%). Parameter estimates were unbiased, parameter variability was largely explicable, and no sample covariance matrices were nonpositive definite except for 50% missing…

Considers models incorporating principal components from the perspectives of structural-equation modeling. These models include the following: (1) the principal-component analysis of patterned matrices; (2) multiple analysis of variance based on principal components; and (3) multigroup principal-components analysis. Discusses fitting these models…

Problems found in the application of structural equation modeling to the theory of reasoned action are explored, and an alternative model specification is proposed that improves the fit of the data while leaving intact the structural part of the model being tested. Problems and the proposed alternative are illustrated. (SLD)

A theoretical and philosophical revision of the concept of fit in structural equation modeling and its relation to a confirmation bias is developed. The neutral character of fit indexes regarding this issue is argued, concluding that protection against confirmation bias relies on model modification strategy and scientist behavior. (SLD)