A logistic regression analysis approach for sample survey data based on phi-divergence measures

TL;DR

This paper introduces a new family of estimators for binary logistic regression models based on phi-divergence measures, extending existing methods to complex survey designs and demonstrating improved efficiency through simulations.

Contribution

It proposes the pseudo minimum phi-divergence estimator family for survey data, extending traditional methods and showing potential efficiency gains.

Findings

Some PMφEs outperform PMLE in efficiency

The new estimators are applicable to complex survey designs

Simulation results support improved performance

Abstract

A new family of minimum distance estimators for binary logistic regression models based on $\phi$-divergence measures is introduced. The so called "pseudo minimum phi-divergence estimator"(PM$\phi$E) family is presented as an extension of "minimum phi-divergence estimator" (M$\phi$E) for general sample survey designs and contains, as a particular case, the pseudo maximum likelihood estimator (PMLE) considered in Roberts et al. \cite{r}. Through a simulation study it is shown that some PM$\phi$Es have a better behaviour, in terms of efficiency, than the PMLE.