Pseudo minimum phi-divergence estimator for multinomial logistic regression with complex sample design

TL;DR

This paper introduces pseudo minimum phi-divergence estimators for multinomial logistic regression with complex sampling, demonstrating their effectiveness through simulations and proposing new estimators for overdispersion and intra-cluster correlation.

Contribution

It develops a theoretical framework for pseudo minimum phi-divergence estimators in complex sample designs and proposes new estimators for overdispersion and intra-cluster correlation.

Findings

Pseudo minimum Cressie-Read divergence estimator with lambda=2/3 performs well.

New estimators effectively handle overdispersion in multinomial logistic regression.

Binder's method excels for intra-cluster correlation coefficient estimation.

Abstract

This article develops the theoretical framework needed to study the multinomial logistic regression model for complex sample design with pseudo minimum phi-divergence estimators. Through a numerical example and simulation study new estimators are proposed for the parameter of the logistic regression model 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 results show 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 = 2/3 , is plugged.