40-Year-Old Asymptotic Distribution Free Estimator Reliably Improves Structural Equation Modeling Statistics for Non-Normal Data

• In Event: Methodology and Application in Structural Equation Modeling

Abstract

In structural equation modeling, researchers conduct goodness-of-fit tests to evaluate whether the specified model fits the data well. With nonnormal data, the standard goodness-of-fit test statistic T does not follow a chi-square distribution. To improve model fit statistics for nonnormal data, we propose to use an unbiased asymptotic distribution free (ADF) estimator {gamma_ADF^U}^hat. Specifically, using normal theory based parameter estimates with {gamma_ADF^U}^hat, we calculate various robust test statistics and robust standard errors. A simulation compared 63 existing robust statistic combinations and 3 robust statistics with {gamma_ADF^U}^hat. The Satorra–Bentler statistic T_SB based on {gamma_ADF^U}^hat (T_SB^U) provided acceptable Type I error rates at alpha=.01, .05, or .1 across all conditions (except a few cases), regardless of the sample size and the distribution.

Authors

• Han Du, University of California - Los Angeles

• Peter Bentler