Minimum phi-divergence estimators for multinomial logistic regression with complex sample design

This article develops the theoretical framework needed to study the multinomial regression model for complex sample design with pseudo-minimum phi-divergence estimators. The numerical example and the simulation study propose new estimators for the parameter of the logistic regression with overdispersed multinomial distributions for the response variables, the pseudo-minimum Cressie–Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The simulation study shows that the Binder’s method for the intra-cluster correlation coefficient exhibits an excellent performance when the pseudo-minimum Cressie–Read divergence estimator, with \(\lambda =\frac{2}{3}\), is plugged.