On the maximum likelihood degree of linear mixed models with two variance components

TL;DR

This paper extends the understanding of the maximum likelihood degree in linear mixed models with two variance components, confirming conjectures and providing bounds for more complex models.

Contribution

It generalizes previous results to models with two variance components and proves conjectures under mild conditions.

Findings

Upper bounds for ML and REML degrees established

Conjecture 1 confirmed for extended models

Results applicable under mild assumptions

Abstract

We extend the results concerning the upper bounds for the maximum likelihood degree and the REML degree of the one-way random effects model presented in Gross et al. [Electron. J. Stat. 6 (2012), pp. 993-1016] to the case of the normal linear mixed model with two variance components. Then we prove that both parts of Conjecture 1 in the paper of Gross et al., which concerns a certain extension of the one-way random effects model, are true under fairly mild conditions.