Robust ANCOVA using a smoother with bootstrap bagging

Many robust analogs of the classic analysis of covariance (ANCOVA) method have been proposed, some of which are based on some type of regression smoother. A method that first appeared in this journal, which is relatively simple and performs well in simulations, is based on a running interval smoother combined with comparing medians or 20% trimmed means. It makes no parametric assumption about the regression lines and does not assume that the regression lines are parallel. A possible way of improving the efficiency of the running interval smoother is to use bootstrap bagging and a minor goal here is to report some results supporting this approach. The major goal is to consider how ANCOVA might be performed when bootstrap bagging is used. Simple extensions of extant approaches that use some type of bootstrap method were found to be unsatisfactory. However, a basic percentile bootstrap method was found to perform well in simulations. And a reanalysis of data dealing with teachers' expectations about the cognitive ability of students illustrates that bootstrap bagging can make a practical difference.