A Comparison of Diagonal Weighted Least Squares Robust Estimation Techniques for Ordinal Data

This study compared diagonal weighted least squares robust estimation techniques available in 2 popular statistical programs: diagonal weighted least squares (DWLS; LISREL version 8.80) and weighted least squares-mean (WLSM) and weighted least squares-mean and variance adjusted (WLSMV; Mplus version 6.11). A 20-item confirmatory factor analysis was estimated using item-level ordered categorical data. Three different nonnormality conditions were applied to 2-to 7-category data with sample sizes of 200, 400, and 800. Convergence problems were seen with nonnormal data when DWLS was used with few categories. Both DWLS and WLSMV produced accurate parameter estimates; however, bias in standard errors of parameter estimates was extreme for select conditions when nonnormal data were present. The robust estimators generally reported acceptable model-data fit, unless few categories were used with nonnormal data at smaller sample sizes; WLSMV yielded better fit than WLSM for most indices.