Examination of the Weighted Root Mean Square Residual: Evidence for Trustworthiness?

This study examined the performance of the weighted root mean square residual (WRMR) through a simulation study using confirmatory factor analysis with ordinal data. Values and cut scores for the WRMR were examined, along with a comparison of its performance relative to commonly cited fit indexes. The findings showed that WRMR illustrated worse fit when sample size increased or model misspecification increased. Lower (i.e., better) values of WRMR were observed when nonnormal data were present, there were lower loadings, and when few categories were analyzed. WRMR generally illustrated expected patterns of relations to other well-known fit indexes. In general, a cutoff value of 1.0 appeared to work adequately under the tested conditions and the WRMR values of good fit were generally in agreement with other indexes. Users are cautioned that when the fitted model is misspeficifed, the index might provide misleading results under situations where extremely large sample sizes are used.