Power of χ2 goodness-of-fit tests in structural equation models:: the case of non-normal data

In the context of structural equation models, we investigate the asymptotic and finite sample size distribution of competing chi(2) goodness-of-fit test statistics. We allow for a) the data to be non-normal, b) the estimation method to be non-optimal, and c) the model to be misspecified. Power of the test is computed distinguishing whether asymptotic robustness (AR) holds or not. The power of the various test statistics is compared, asymptotically and using Monte Carlo simulation. A scaled version of a normal-theory (NT) goodness-of-fit test statistic for ULS analysis is included among the test statistics investigated.