  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. Robust testing of general linear hypotheses on the
regression coefficients are proposed using the new estimators. Their asymptotic
distributions and robustness properties are theoretically studied and also
empirically validated through a numerical example and an extensive Monte Carlo
study.
