Full weighted least squares (full WLS) and robust weighted least squares (robust
WLS) are currently the two primary estimation methods designed for structural equation
modeling with ordinal observed variables. These methods assume that continuous latent
variables were coarsely categorized by the measurement process to yield the observed
ordinal variables, and that the model proposed by the researcher pertains to these latent
variables rather than to their ordinal manifestations.
Previous research has strongly suggested that robust WLS is superior to full WLS
when models are correctly specified. Given the realities of applied research, it was
critical to examine these methods with misspecified models. This Monte Carlo simulation
study examined the performance of full and robust WLS for two-factor, eight-indicator confirmatory factor analytic models that were either correctly specified, overspecified, or
misspecified in one of two ways. Seven conditions of five-category indicator distribution
shape at four sample sizes were simulated. These design factors were completely crossed
for a total of 224 cells.
Previously findings of the relative superiority of robust WLS with correctly
specified models were replicated, and robust WLS was also found to perform better than
full WLS given overspecification or misspecification. Robust WLS parameter estimates
were usually more accurate for correct and overspecified models, especially at the
smaller sample sizes. In the face of misspecification, full WLS better approximated the
correct loading values whereas robust estimates better approximated the correct factor
correlation. Robust WLS chi-square values discriminated between correct and
misspecified models much better than full WLS values at the two smaller sample sizes.
For all four model specifications, robust parameter estimates usually showed lower
variability and robust standard errors usually showed lower bias.
These findings suggest that robust WLS should likely remain the estimator of
choice for applied researchers. Additionally, highly leptokurtic distributions should be
avoided when possible. It should also be noted that robust WLS performance was
arguably adequate at the sample size of 100 when the indicators were not highly
leptokurtic. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/6610 |
| Date | 22 October 2009 |
| Creators | Vaughan, Phillip Wingate |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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