suppose I have a case study with 3 different populations, A, B and C. For all groups I have data on, e.g. body mass, length and sex of a given species. For group A I also have information on the year of birth, which I may be interested to include in the analysis as a random term to account for the cohort effect, while for groups B and C I have no such information. The dataframe would look something like:

Pop Coh Weight Length Sex

A 2010 12.1 34 m

A 2011 13.4 42 m

A 2012 10.3 36 f

A 2010 10.5 32 m

A 2013 12.1 37 f

A 2014 12.4 35 f

A 2011 14.1 32 f

...

B NA 13.1 36 m

B NA 10.5 35 f

B NA 12.4 32 f

B NA 12.6 35 m

...

C NA 13.7 31 m

C NA 11.5 37 f

C NA 10.7 33 m

C NA 11.9 35 f

...

Let's now suppose I want to investigate the relationship between Weight and Length, for males and females of different populations, e.g. by using a 3-way interaction. Would it still be possible to run the analysis in one single mixed model with a random intercept (cohort) only for group A?

With my actual dataset, the model

lmer(Weight ~ Length * Sex * Pop + (1 + Pop | Coh) )

fitted changing NAs to 1 appears to work, as it returns the same estimates for population B and C (but clearly not A) as the model

lm(Weight ~ Length * Sex * Pop)

but I am not quite sure if this is the correct approach.

Thanks!