Hi,
I just came across the following issue regarding mixed effects models:
In a longitudinal study individuals (variable ind) are observed for some
response variable. One explanatory variable, f, entering the model as
fixed effect, is a (2-level) factor. The expression of that factor is
constant for each individual across time (say, the sex of the
individual). ind enters the model as grouping variable for random
effects. So in a simple form, the formula could look like:
y ~ f + ... + (1|ind)
[and in the simplest model, the ellipsis is simply nothing]
To me, this seems not to be an unusual design at all.
However, the indicator matrix consisting of f and ind - say if ind had
entered the model as fixed effect - shows a singularity. My question is
now what will this 'singularity' cause in a mixed-effects model ? I
admit, I have never fully understood how the fitting of mixed-effects
models happen internally (whether REML or ML) [so I am not even sure if
it can be called a 'singularity'].
Specifically, does it make the fit numerically more unstable? Would the
degree of this depend on other variables of the model? Is the issue of
degrees of freedom - complicated enough anyway for mixed models -
further inflated by that? Have statistical inferences regarding the
fixed effect be treated more carefully? Is the general situation
something that should be avoided ?
many thanks in advance for any insights and cheers,
Thomas
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