title: Measuring and detecting associations: methods based on robust regression estimators or smoothers that allow curvature.
abstract: This paper considers the problem of estimating the overall strength of an association, including situations where there is curvature. The general strategy is to fit a robust regression line, or some type of smoother that allows curvature, and then use a robust analogue of explanatory power, say eta(2). When the regression surface is a plane, an estimate of eta(2) via the Theil-Sen estimator is found to perform well, relative to some other robust regression estimators, in terms of mean squared error and bias. When there is curvature, a generalization of a kernel estimator derived by Fan performs relatively well, but two alternative smoothers have certain practical advantages. When eta(2) is approximately equal to zero, estimation using smoothers has relatively high bias. A variation of eta(2) is suggested for dealing with this problem. Methods for testing H(0): eta(2)=0 are examined that are based in part on smoothers. Two methods are found that control Type I error probabilities reasonably well in simulations. Software for applying the more successful methods is provided.
authors.affiliation: Department of Psychology, University of Southern California, Los Angeles, California 90089, USA. rwilcox@usc.edu
authors.forename: Rand R
authors.initials: RR
authors.lastname: Wilcox
mesh_terms: D001245:Association Learning; D015982:Bias; D002096:C-Peptide / Q000097:blood; D002648:Child; D003196:Computer Graphics; D003198:Computer Simulation; D003922:Diabetes Mellitus, Type 1 / Q000097:blood; D006801:Humans; D008432:Mathematical Computing; D011930:Reaction Time; D011932:Reading; D012044:Regression Analysis; D013223:Statistics as Topic; D014705:Verbal Behavior
chemical_list: D002096:C-Peptide