How to build a GLMM that observes the years since experimental design was established?

Question

Hello, my first question, quite individual, so I find it difficult to relate already answered questions to mine.

I have observed the vegetation development in forests of 5 different areas (area) in an experimental experiment. The design can be classified according to 3 types of size and distribution (treatment) including control plot, and the occurrence of deadwood with 5 types including control plot. For each treatment there is every option of deadwood and vice versa. The data have been collected for 4 years (years -> 1y-4y). Five microclimate variables (mc1-5) are included as fixed effects. As random effects I would like to include area, treatment and deadwood. With regard to vegetation development it is interesting how the effects of microclimate (mc1-5), but especially of treatment and deadwood have changed over the years. In area the factor years should be negligible. As I understand it, years and treatment /deadwood are nested, because the same plots are examined every year.

My previous attempt to build a model:

glmm <- glmer(species.number ~ mc1 + mc2 + mc3 + mc4 + mc5 + 
              (1|treatment/years) + (1|deadwood/years) + (1|area), 
              data=df, family = poisson)

Among other things, I am confused by this actually very good answer that in my case it might be crossed data after all?

Thanks a lot!

Answer 1

The central interest is in the "effects" of the microclimate variables, and whether these change over time. As such, time should be treated as a fixed effect. Treating it as random will only allow for counts to be more similar in one year than another. Interacting year with the microclimate variables will help to answer the research questions.

area seems to meet the usual criteria for treating a factor as random - samples from a greater population of areas, with no actual interest in the "effects" of the different areas, with the exception of the number of areas. 5 is on the cusp of what is generally thought of as the minimum number of levels for treating a factor as random in the frequentist paradigm. It could be argued either way whether it should be random or not.

From the description in the comments, treatment and deadwood appear to be factors that are crossed, but each nested within area. They don't really seem like samples from a wider population, however this is not crucial as there are often conflicting criteria (and other criteria I haven't mentioned). Since they are nested within area, we don't need to worry about them having only 3 and 5 levels.

So the model I would suggest is:

species.number ~ mc1*year + mc2*year + mc3*year + mc4*year + mc5*year + (1|area) + (1|area:treatment) + (1|area:deadwood)

If you expect a linear association of the counts with time, then it would be a good idea to treat year as numeric (0,1,2,3), particularly if the microclimate variables are categorical, otherwise you will have a lot of output to interpret.

Lastly I would also suggest some consideration about whether there is an causual dependence among any of the fixed or random effects - are all the microclimate variables independent from each other and the the treatment and deadwood variables.