Examining the Performance of the Modified ADF Goodness-of-fit Test Statistic in Structural Equation Models

The asymptotically distribution-free (ADF) test statistic depends on very mild distributional assumptions and is theoretically superior to many other so-called robust tests available in structural equation modeling. The ADF test, however, often leads to model overrejection even at modest sample sizes. To overcome its poor small-sample performance, a family of robust test statistics obtained by modifying the ADF statistics was recently proposed. This study investigates by simulation the performance of the new modified test statistics. The results revealed that although a few of the test statistics adequately controlled Type I error rates in each of the examined conditions, most performed quite poorly. This result underscores the importance of choosing a modified test statistic that performs well for specific examined conditions. A parametric bootstrap method is proposed for identifying such a best-performing modified test statistic. Through further simulation it is shown that the proposed bootstrap approach performs wel