[R-sig-ME] defining nested and crossed random effects in glmer

[Eskelinen, Anu]

Hello,

I have a question related to defining a random formula in a mixed effects model in glmer. I would be grateful for any help from this expert community. Thanks a lot already in advance!

My question relates to ecological plant species data from a full-factorial experiment with four treatments. In the experiment, treatment 1 is nested within treatments 2 and 3, and treatments 2 and 3 are nested within treatment 4. All treatments have two levels (manipulation, no manipulation). Treatment 1 subplots (manipulation, no manipulation) are next to each other (paired), forming bigger plots that receive a combination of treatments 2 and 3. These plots are arranged in groups of four (called blocks) that receive treatment 4. Pretty complex experiment, yes, as many ecological questions are complex.

My question concerns the following analysis. We have calculated a binary 0-1 response variable between the subplots for plant species that occur in the subplots. We call this �species responsiveness to treatment 1�. We then explain this �species responsiveness to treatment 1� by treatments 2, 3 and 4, and by an additional continuous variable which is a trait that describes some characteristics of the species. The main question is to assess whether species� traits affect their responsiveness to treatment 1, and whether species traits and other treatments interact to affect their responsiveness to treatment 1.

I have used this model in R to examine the above question:

model <- glmer(species_responsiveness ~ (treatment4+treatment3+treatment2+trait)^3 + (1|block/plot), family=binomial, data=traits)

As far as I understand, this random structure should take into account that 1) species observations are nested within plots, and 2) plots are nested within blocks. There are multiple species occurring in the same plots, that�s why species is nested within plots, and most species also occur in several plots but not all species occur in all plots. There are many species (~40) in the data.

My question is that does the species identity also need to be a crossed random factor in the model? Like this:

+(1|block/plot) + (1|species)

With this random formula, the model would be:

model <- glmer(species_responsiveness ~ (treatment1+treatment2+treatment3+trait)^3 + (1|block/plot) + (1|species), family=binomial, data=traits)

However, with this random structure I get a lot of complaints and sometimes the models do not converge at all. Models without species converge normally. Scaling the trait values does not help. I have several traits for the species, each analyzed in its own model, and they are all performing equally badly. I get, for example, these error messages:

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge with max|grad| = 0.0841993 (tol = 0.002, component 1)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
Or
Model failed to converge with max|grad| = 0.0841993 (tol = 0.002, component 1)
Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?

In the data, �species� overlaps/aligns perfectly with �trait� as each individual species has only one unique value for each trait. Here�s an example how it can look in the data:

species      trait
Antodo       0.2
Antodo       0.2
Antodo       0.2
Helpra       0.5
Helpra       0.5
Helpra       0.5
Seqvar       0.03
Seqvar       0.03
Seqvar       0.03

So, when I have �trait� as a fixed factor and �species� as a random factor, do they compete to explain the same variation in the data? And can that be causing problems in model convergence? What kind of random formula would be correct? I would be super grateful for any advice/thoughts. Thanks so much!

Best regards,
Anu

Assoc. Prof. Anu Eskelinen
Oulu University, Finland
iDiv and UFZ, Leipzig, Germany



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