Comparing the Strength of Association of Two Predictors via Smoothers or Robust Regression Estimators

Authors

Rand R. Wilcox, University of Southern CaliforniaFollow

Abstract

Consider three random variables, Y , X₁ and X₂, having some unknown trivariate distribution and let n²_j (j = 1, 2) be some measure of the strength of association between Y and X_j. When n²_j is taken to be Pearson’s correlation numerous methods for testing H_o : n²₁ = n²₂ have been proposed. However, Pearson’s correlation is not robust and the methods for testing H₀ are not level robust in general. This article examines methods for testing H₀ based on a robust fit. The first approach assumes a linear model and the second approach uses a nonparametric regression estimator that provides a flexible way of dealing with curvature. The focus is on the Theil-Sen estimator and Cleveland’s LOESS smoother. It is found that a basic percentile bootstrap method avoids Type I errors that exceed the nominal level. However, situations are identified where this approach results in Type I error probabilities well below the nominal level. Adjustments are suggested for dealing with this problem.

DOI

10.22237/jmasm/1304222520