Hi,

I am looking at a two-way random-effects ANOVA layout as a particular case
of the general mixed-model,

y|b ~ N(X beta + Zb, sigsq I)
b ~ N(0,sigsq Gamma_theta )    [Gamma diagonal],

I am trying to compute ML estimates for theta under a KNOWN sigsq (i.e.,
error variance is known). I derived my own ML estimates since lmer()
estimates sigsq rather than assuming it is known.
As long as the variance components (or theta's) are "big" (far from zero),
the output of my algorithm is consistent with the output of lmer (when
plugging in the estimated sigsq into my functions); but I run into problems
when the ML estimates for at least one of the theta's is close zero.

Before i roll up my sleeves, I would like to know how lmer handles the case
in which the value of theta which nullifies the derivative is negative (or
does not exist at all), i.e., the ML estimate cannot be obtained by
searching for a root of the derivative of the profile likelihood.

(If my point was not clear, I refer to the case similar to what happens in
the balanced two-way ANOVA when the row (or column) sum of squares minus
the estimated error component is negative..).

Thanks so much,
Asaf

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