A Note on Using and Unbiased Weight Matrix in the ADF Test Statistic.

In covariance structure analysis, the asymptotically distribution-free (ADF) method fails to work satisfactorily unless the sample is extremely large. Simulation studies report that the ADF test statistics observed arc usually too large and correct models arc then over-rejected. It is known that the accuracy of the ADF test statistic depends on the estimation of the weight matrix. In existing literature and computer software, a biased estimator W is used as an estimate of the unknown weight matrix. In this article. we suggest that W, an unbiased estimate of the weight matrix, may eliminate the small or intermediate sample size bias of the ADF test statistic. Results show that the test statistics based on W and W arc highly similar. The poor performance of the ADF method was not caused by the use of a biased weight matrix in the model studied in this article.