[R-sig-ME] threshold for singular fit

[David Duffy]

Jill Brouwer asks:

> I am trying to fit a GLMM with fixed effect of pH treatment (Chamber), and
> random effects of male, female, male:female, and male:female:treatment
> (interested in assessing differences in compatibility caused by pH). My
> response variable is poisson sperm count data. There are 18 blocks with 2
> replicates per 2x male and female cross in each. Observation level random
> effect added to account for overdispersion.


> countsmodel <- glmer(Count_total ~ Chamber + (1|Block) + (1|Male) +
> (1|Female) + (1|Male:Female) +
>                    (1|Male:Female:Chamber) + (1|Sample), family =
> "poisson", data = counts)

> it gives a singular fit error, however when I run the isSingular function
> Generalized linear mixed model fit by maximum likelihood (Laplace

> My question is: can I interpret any findings from this model given the
> singular fit warning? If not, what is a suitable approach?

You _might_ obtain different results using other than the Laplace approximation. I have been trying the 
the glmmsr package that allows 4 alternatives (importance sampler, sequential reduction, AGQ, Laplace).

> Also, I asked this question before and tried to get help from local
> statisticians, but they didn't know. Is it appropriate to assess the
> significance of the random effects using likelihood ratio testing comparing
> full model to reduced model one random effect at a time? 

Yes, but the distribution of the test statistic is usually some complex mixture of chi-squares. There are packages that can simulate these - or you can do it yourself. You can also just use a conservative ad hoc cutoff. The other way is to go to MCMC packages, one obvious choice being MCMCglmm.

2c, David Duffy.