Quasi-independence models with rational maximum likelihood estimator

TL;DR

This paper classifies two-way quasi-independence models with structural zeros that admit rational maximum likelihood estimators, providing combinatorial conditions and explicit formulas, and extends results to related log-linear models.

Contribution

It offers a complete classification of models with rational MLEs based on bipartite graph properties and extends the rationality results to face-restricted models using Horn uniformization.

Findings

Characterization of bipartite graphs for rational MLEs

Explicit formulas for MLEs in these models

Extension of rational MLE property to face-restricted models

Abstract

We classify the two-way independence quasi-independence models (or independence models with structural zeros) that have rational maximum likelihood estimators, or MLEs. We give a necessary and sufficient condition on the bipartite graph associated to the model for the MLE to be rational. In this case, we give an explicit formula for the MLE in terms of combinatorial features of this graph. We also use the Horn uniformization to show that for general log-linear models $\mathcal{M}$ with rational MLE, any model obtained by restricting to a face of the cone of sufficient statistics of $\mathcal{M}$ also has rational MLE.