Bootstrap approach to inference and power analysis based on three test statistics for covariance structure models.

We study several aspects of bootstrap inference for covariance structure models based on three test statistics, including Type I error, power and sample-size determination. Specifically, we discuss conditions for a test statistic to achieve a more accurate level of Type I error, both in theory and in practice. Details on power analysis and sample-size determination are given. For data sets with heavy tails, we propose applying a bootstrap methodology to a transformed sample by a downweighting procedure. One of the key conditions for safe bootstrap inference is generally satisfied by the transformed sample but may not be satisfied by the original sample with heavy tails. Several data sets illustrate that, by combining downweighting and bootstrapping, a researcher may find a nearly optimal procedure for evaluating various aspects of covariance structure models. A rule for handling non-convergence problems in bootstrap replications is proposed.