Minimum {\phi}-divergence estimation in constrained latent class models for binary data

TL;DR

This paper introduces minimum {}-divergence estimators as a robust alternative to maximum likelihood estimators in binary latent class models, analyzing their properties and comparing performance through simulations.

Contribution

It develops the asymptotic theory for minimum {}-divergence estimators in binary latent class models and evaluates their efficiency and robustness via simulation.

Findings

Minimum {}-divergence estimators are a natural extension of MLE.

The estimators exhibit desirable asymptotic properties.

Simulation shows improved robustness over MLE in small samples.

Abstract

The main purpose of this paper is to introduce and study the behavior of minimum {\phi}-divergence estimators as an alternative to the maximum likelihood estimator in latent class models for binary items. As it will become clear below, minimum {\phi}-divergence estimators are a natural extension of the maximum likelihood estimator. The asymptotic properties of minimum {\phi}-divergence estimators for latent class models for binary data are developed. Finally, to compare the efficiency and robustness of these new estimators with those obtained through maximum likelihood when the sample size is not big enough to apply the asymptotic results, we have carried out a simulation study.