I'm running a SEM model where one latent variable is regressed on four latent variables. All indicators are categorical and the sample comprise about 35 000 cases. In Flora & Curran (2004) it is shown that WLSMV perform better than WLS in small to moderate samples. Will WLSMV outperform WLS in large samples (35 000), are they about equally accurate, or will WLS outperform WLSMV in samples of that size? Do you know of any simulation studies looking into this?
Muthén, B., du Toit, S.H.C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Unpublished technical report.