I am rather puzzled by the results of applying vcov() to (binomial)
models fitted by glmer().? The linear predictor in the models is of the
form
???? alpha_i + beta_i * x + <random effects>
where "i" corresponds to "treatment group" and x is numeric.? There are
six treatment groups so the covariance matrix returned by vcov() is
12 x 12.
When I fit the model with nAGQ = 0 in the call to glmer() the resulting
matrix is quite sparse --- there is non-zero covariance only between
parameter estimates corresponding to the same value of "i" (i.e. to the
same treatment group).? In other words, under the appropriate ordering
of the estimated parameters, the covariance matrix is block diagonal,
with six 2 x 2 blocks.
When I fit the model with nAGQ set equal to 1, the resulting covariance
matrix is non-sparse; all entries are non-zero.? (The entries outside of
the "block diagonal structure" are, I suppose, "relatively" small ---
they range from -0.0145 to 0.0010 --- but are well away from being
"approximately zero".)
I would like a better understanding of the reason for the difference.? I
was under the impression that setting nAGQ = 0 gives a somewhat
quick-and-dirty fit of the model; less accurate and reliable than with
nAGQ = 1.? Why does setting nAGQ = 0 (apparently) cause the covariance
between parameter estimates corresponding to different treatment groups
to be *exactly* zero?
If I remember my childhood teaching correctly, in a *linear* model, such
covariances would indeed be exactly zero, so one might expect
"approximately" zero in the generalised linear model setting.? But why
should setting nAGQ = 0 result in a covariance matrix which is "just
like" one from the linear model setting?
I guess it doesn't really matter a damn, but I'd like to understand what
is going on, at least "in rough intuitive terms".
Can anyone enlighten me?
Thanks.
cheers,
Rolf Turner