A Note on the Identifiability of Generalized Linear Mixed Models

TL;DR

This paper provides a simple proof demonstrating the identifiability of standard parametrizations in generalized linear mixed models under general regularity conditions, extending to quasi-likelihood models including binomial and Poisson cases.

Contribution

It offers a straightforward proof of identifiability for generalized linear mixed models, applicable to a broad class including quasi-likelihood models.

Findings

Standard parametrization is identifiable under regularity conditions.

Identifiability extends to binomial and Poisson mixed models with dispersion.

Proof is based on moments and regularity assumptions.

Abstract

I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first and second order moments and some general mild regularity conditions, and, therefore, is extensible to quasi-likelihood based generalized linear models. In particular, binomial and Poisson mixed models with dispersion parameter are identifiable when equipped with the standard parametrization.