[R] 'singularity' between fixed effect and random factor in mixedmodel

[Daniel Malter]

An Econometrician may help you with more theoretical insights, but you could
do Monte-Carlo simulations of data and analyze the effects you are
interested in.

Daniel

-------------------------
cuncta stricte discussurus
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-----Ursprüngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von Thomas Mang
Gesendet: Wednesday, July 01, 2009 7:53 PM
An: r-help at stat.math.ethz.ch
Betreff: [R] 'singularity' between fixed effect and random factor in
mixedmodel

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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