Robust semiparametric inference for polytomous logistic regression with complex survey design

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is a robust generalization of the maximum quasi weighted likelihood estimator exploiting the advantages of the popular density power divergence measure. Accordingly robust estimators for the design effects are also derived. Using the new estimators, robust testing of general linear hypotheses on the regression coefficients are proposed. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo study.