Testing Model Fit by Bootstrap Selection

Over the last few decades, many robust statistics have been proposed in order to assess the fit of structural equation models. To date, however, no clear recommendations have emerged as to which test statistic performs best. It is likely that no single statistic will universally outperform all contenders across all conditions of data, sample size, and model characteristics. In a real-world situation, a researcher must choose which statistic to report. We propose a bootstrap selection mechanism that identifies the test statistic that exhibits the best performance under the given data and model conditions among any set of candidates. This mechanism eliminates the ambiguity of the current practice and offers a wide array of test statistics available for reporting. In a Monte Carlo study, the bootstrap selector demonstrated promising performance in controlling Type I errors compared to current test statistics.