Phi-Divergence test statistics for testing the validity of latent class models for binary data

TL;DR

This paper introduces phi-divergence based test statistics for assessing the goodness-of-fit of latent class models for binary data, providing asymptotic distributions and simulation-based efficiency comparisons.

Contribution

It presents new families of test statistics based on phi-divergence measures for latent class model validation, extending the existing maximum likelihood approach.

Findings

New test statistics based on phi-divergence are developed.

Asymptotic distributions of the test statistics are derived.

Simulation studies compare the efficiency of the new tests.

Abstract

The main purpose of this paper is to present new families of test statistics for studying the problem of goodness-of-fit of some data to a latent class model for binary data. The families of test statistics introduced are based on phi-divergence measures, a natural extension of maximum likelihood. We also treat the problem of testing a nested sequence of latent class models for binary data. For these statistics, we obtain their asymptotic distribution. We shall consider consistent estimators introduced in Felipe et al (2014) for solving the problem of estimation. Finally, a simulation study is carried out in order to compare the efficiency, in the sense of the level and the power, of the new statistics considered in this paper for sample sizes that are not big enough to apply the asymptotical results.