On the maximum likelihood estimation in general log-linear models

TL;DR

This paper introduces a new iterative scaling method for maximum likelihood estimation in general log-linear models without the overall effect, demonstrating its convergence and practical application.

Contribution

It proposes a novel iterative scaling algorithm for MLE in log-linear models lacking the overall effect, with proven convergence and real-data illustration.

Findings

Convergence of the proposed iterative scaling method is established.

The method effectively estimates parameters in models without the overall effect.

Application to clinical data demonstrates practical utility.

Abstract

General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a normalizing constant, is still rare. The log-linear models without the overall effect arise naturally in practice, and can be handled in a similar manner to models with the overall effect. A novel iterative scaling procedure for the MLE computation under such models is proposed, and its convergence is proved. The results are illustrated using data from a recent clinical study.