Nonparametric bootstrap tests of conditional independence in two-way contingency tables

Abstract

a b s t r a c tWhen analyzing a two-way contingency table, a preliminary question is often whether the categorical variables under study, say R and S, are independent or not. Suppose now that for each individual in the table, a continuous variable X is also known. It is then worth analyzing the table conditionally on X . Contrasting these ''local'' results to the global unconditional case allows one to go beyond the initial analysis and provide a better understanding of the underlying phenomenon. Recently, Geenens and Simar (2010) [11] have proposed two nonparametric procedures for testing whether R and S are conditionally independent given X , free of any constraining linearity assumptions. However, based on an average of kernel-based estimators, the asymptotic criterion they suggested shows an inflated Type I error (false positive) for small to moderate sample sizes. In this paper, we address this problem by proposing consistent bootstrap versions of the Geenens-Simar test procedures when testing for local independence. A comprehensive simulation study indeed shows the superiority of the bootstrap rejection criterion as compared to the asymptotic criterion in terms of Type I error. It also highlights the advantage of the flexibility guaranteed by the nonparametric Geenens-Simar tests when compared with parametric competitors, e.g. logistic models. The approach is finally illustrated with a realdata example.

A nonparametric measure of local association for two-way contingency tables

“…To obtain bootstrap based confidence intervals, we propose a new resampling procedure called the multinomial-1 bootstrap, inspired by some ideas in Rodriguez-Campos and Cao-Abad (1993) and developed in Hui and Geenens (2012).…”