Semiparametric clustered overdispersed multinomial goodness-of-fit of log-linear models

TL;DR

This paper develops new distribution-free goodness-of-fit tests for log-linear models applied to clustered contingency tables, accounting for potential intra-cluster correlation without relying on the Dirichlet-multinomial assumption.

Contribution

It introduces novel test-statistics that do not depend on specific distributional assumptions, utilizing an estimator for intracluster correlation across varying cluster sizes.

Findings

New test-statistics effectively test log-linear hypotheses without distributional constraints

The proposed methods accommodate homogeneously correlated individuals within clusters

The approach extends goodness-of-fit testing beyond Dirichlet-multinomial models

Abstract

Traditionally, the Dirichlet-multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes. There are, however, other possible distributions appropriate for these contingency tables. This paper introduces new test-statistics capable to test log-linear modeling hypotheses with no distributional specification, when the individuals of the clusters are possibly homogeneously correlated. The estimator for the intracluster correlation coefficient proposed in Alonso-Revenga et al. (2016), valid for different cluster sizes, plays a crucial role in the construction of the goodness-of-fit test-statistic.