Effect of estimation method on incremental fit indexes for covariance structure models

In a typical study involving covariance structuremodeling, fit of a model or a set of alternativemodels is evaluated using several indicators of fitunder one estimation method, usually maximumlikelihood. This study examined the stability acrossestimation methods of incremental and nonincrementalfit measures that use the informationabout the fit of the most restricted (null) model asa reference point in assessing the fit of a moresubstantive model to the data. A set of alternativemodels for a large empirical dataset was analyzedby asymptotically distribution-free, generalizedleast squares, maximum likelihood, and ordinaryleast squares estimation methods. Four incrementaland four nonincremental fit indexes were compared.Incremental indexes were quite unstableacross estimation methods-maximum likelihoodand ordinary least squares solutions indicatedbetter fit of a given model than asymptoticallydistribution-free and generalized least squares solutions.The cause of this phenomenon is explainedand illustrated, and implications and recommendationsfor practice are discussed. Index terms:covariance structure models, goodness of fit,incremental fit index, maximum likelihood estimation,parameter estimation, structural equation models.