Robust Wald-type methods for testing equality between two populations regression parameters: A comparative study under the logistic model

Comparing the regression parameters between two populations is useful to understand the homogeneity of the process underlying the data. The problem of logistic regression is considered when the practitioner handles data from two populations and when the goal is to test the hypothesis that some regression parameters are equal in both populations. A classical testing procedure is to construct a Wald-type test from the maximum likelihood estimators obtained from each data set. However, as in the one-population setting, the presence of outliers in any of the two samples may distort both the level and/or the power of this procedure. Instead of the maximum likelihood procedure, reliable statistics are built using a class of robust estimators which bound large values of the deviance as well as the effect of high leverage points. The asymptotic behaviour of this family of test statistics is derived under the null and contiguous alternatives. Besides, the robustness of the tests is investigated through the influence function. A simulation study allows to compare, under different contamination schemes, the behaviour of the tests based on the maximum likelihood estimators and on their robust counterparts. The numerical study shows that the Wald tests based on the maximum likelihood estimators or on the unweighted robust ones break down when atypical data arise in the samples, while both the level and power of the Wald-type tests based on redescending weighted M−estimators are stable against the considered contaminations. The analysis of a real data set enables to investigate the p− value sensitivity to the presence of outliers.