A question about multicollinear fixed/random factors

If I'm understanding this right, I don't think there is a problem at all.
Mixed-effects models can accommodate fixed effects at different levels 
and these can coexist with the random effects without any issues. 
Number of days is simply a 'Level-2' predictor, with a unique value 
for each meeting.

(for more complex random-effects structures, you might want to 
consider the inclusion of session as another random factor and/or of 
by-word random slopes)

Jo?o

On 20/08/2022 09:40, N o s t a l g i a wrote:

Hi,

I am looking at a character variation in Japanese parliamentary 
minutes where the same character appears in two forms. In the 
parliament, there are a number of different committee meetings 
within the same session, and I am looking at 31 sessions over 10 
years. The factors I am considering are: upper/lower house 
distinction, meetings (meetings within each session, which are 
different from session to session), days between 1949/5/20 (when the 
first parliament was held) and the meeting, and the word within 
which the character appears. Of these, meetings and the words are 
random factors, and they have hundreds of levels. The total number 
of cases is over one million.

The model I am considering is:

glmer (character ~ ul + days + (1|word) + (1|meeting), data = 
glmmdata.1, family = binomial)

And here is my question: Since a given meeting is a unique one not 
only in each session but in all the data, there would be a 
multicollinear relationship between the days and the meeting, so 
that specification of some meeting would necessarily result in a 
specific value of days. Is it a problem in GLMM to have such pair of 
fixed and random factors? If it is so, is there any ways to avoid 
the problem?

Thanks in advance,

Kenjiro Matsuda
Professor in Linguistics
Kobe Shoin Women's University
Kobe, Japan