[R-sig-ME] threshold for singular fit

[Jill Brouwer]

Hi all,

Is there an acceptable threshold for singular fits?

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.

When I try and fit this full model:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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
on the model with default threshold (1x10^-5), it comes out false. Below is
the model summary output. The singular fit warning is probably coming from
the low variance of male:female random effect.

Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: poisson  ( log )
Formula: Count_total ~ Chamber + (1 | Block) + (1 | Male) + (1 | Female) +
    (1 | Male:Female) + (1 | Male:Female:Chamber) + (1 | Sample)
   Data: counts

     AIC      BIC   logLik deviance df.resid
  2941.8   2971.1  -1462.9   2925.8      280

Scaled residuals:
       Min         1Q     Median         3Q        Max
-2.0097349 -0.1649262  0.0246676  0.1418016  0.6601243

Random effects:
 Groups              Name        Variance    Std.Dev.
 Sample              (Intercept) 9.98380e-02 3.15971e-01
 Male:Female:Chamber (Intercept) 1.36128e-02 1.16674e-01
 Male:Female         (Intercept) 5.92690e-09 7.69864e-05
 Female              (Intercept) 3.84069e-03 6.19733e-02
 Male                (Intercept) 9.82313e-02 3.13419e-01
 Block               (Intercept) 2.87611e-02 1.69591e-01
Number of obs: 288, groups:
Sample, 288; Male:Female:Chamber, 144; Male:Female, 72; Female, 36; Male,
36; Block, 18

Fixed effects:
              Estimate Std. Error  z value Pr(>|z|)
(Intercept) 4.54183984 0.07348953 61.80254  < 2e-16 ***
Chamberlow  0.00964211 0.04389841  0.21965  0.82615
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
           (Intr)
Chamberlow -0.299
convergence code: 0
boundary (singular) fit: see ?isSingular
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
My question is: can I interpret any findings from this model given the
singular fit warning? If not, what is a suitable approach?

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? For example, can I
test for significance of M:F two-way interaction, whilst leaving in the
male:female:treatment higher order three way interaction? Does the Drop1
approach apply to random effects in GLMMs?

Kind regards,
Jill

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