  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.
