Confirmatory factor analysis with ordinal data : effects of model misspecification and indicator nonnormality on two weighted least squares estimators

Full weighted least squares (full WLS) and robust weighted least squares (robustWLS) are currently the two primary estimation methods designed for structural equationmodeling with ordinal observed variables. These methods assume that continuous latentvariables were coarsely categorized by the measurement process to yield the observedordinal variables, and that the model proposed by the researcher pertains to these latentvariables rather than to their ordinal manifestations.Previous research has strongly suggested that robust WLS is superior to full WLSwhen models are correctly specified. Given the realities of applied research, it wascritical to examine these methods with misspecified models. This Monte Carlo simulationstudy examined the performance of full and robust WLS for two-factor, eight-indicator confirmatory factor analytic models that were either correctly specified, overspecified, ormisspecified in one of two ways. Seven conditions of five-category indicator distributionshape at four sample sizes were simulated. These design factors were completely crossedfor a total of 224 cells.Previously findings of the relative superiority of robust WLS with correctlyspecified models were replicated, and robust WLS was also found to perform better thanfull WLS given overspecification or misspecification. Robust WLS parameter estimateswere usually more accurate for correct and overspecified models, especially at thesmaller sample sizes. In the face of misspecification, full WLS better approximated thecorrect loading values whereas robust estimates better approximated the correct factorcorrelation. Robust WLS chi-square values discriminated between correct andmisspecified models much better than full WLS values at the two smaller sample sizes.For all four model specifications, robust parameter estimates usually showed lowervariability and robust standard errors usually showed lower bias.These findings suggest that robust WLS should likely remain the estimator ofchoice for applied researchers. Additionally, highly leptokurtic distributions should beavoided when possible. It should also be noted that robust WLS performance wasarguably adequate at the sample size of 100 when the indicators were not highlyleptokurtic.