[R-sig-ME] threshold for singular fit

[Ben Bolker]

  Agree with David's points below.  A couple of points:

  * the GLMMadaptive package provides an alternative way to fit
non-Laplace models (AGQ)
  * that said, I'd be surprised if different approximations did away
with the singularity problem.  You've got a medium-sized data set (I'm
not sure whether you have 8 or 4 observations per block, but at most 144
observations), and you're trying to partition the variability into 6
components (plus the intrinsic Poisson variability).
  * it's true that the null distribution of the differences in
log-likelihoods is complicated, but in those cases where one of the
variance terms is estimated as zero it's unlikely (impossible?) that it
will be significant no matter what you do ...

  Parametric bootstrapping via PBmodcomp() in the pbkrtest package will
be more or less the gold standard for frequentist testing of
random-effect variances (it'll be slow, since it requires refitting
models hundreds of times per model comparison).
   You might try a few PBmodcomp() tests and compare them against the
likelihood ratio test results to see how much difference it makes/how
much it's worth the hassle of the extra computation.

  Bayesian methods will allow you to add regularizing terms to avoid
singular fits, but will also complicate your task of computing p-values ...

On 2020-02-05 6:37 p.m., David Duffy wrote:
> 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.
> 
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