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Analyzing polytomous response from a complex survey scheme, like stratifiedor cluster sampling is very crucial in several socio-economics applications. Wepresent a class of minimum quasi weighted density power divergence estimatorsfor the polytomous logistic regression model with such a complex survey. Thisfamily of semiparametric estimators is a robust generalization of the maximumquasi weighted likelihood estimator exploiting the advantages of the populardensity power divergence measure. Accordingly robust estimators for the designeffects are also derived. Robust testing of general linear hypotheses on theregression coefficients are proposed using the new estimators. Their asymptoticdistributions and robustness properties are theoretically studied and alsoempirically validated through a numerical example and an extensive Monte Carlostudy.

Robust semiparametric inference for polytomous logistic regression with complex survey design