I have a data set which involves 30 binomial absence/presences totalled for a ratio out of 1, which is the total score of a test out of 30 marks. The data requires fitting one of my predictor variables as a random effect,

glmer1 <- glmer(formula= cbind(NumberPresent, NumberAbsent) ~ Year + 
   Class + Gender + (1|School), data = Framework1, 
   family = "binomial"(link="logit"))

summary(glmer1) gives

AIC  4112.8     
BIC 4135.9
logLik -2051.4
deviance 4102.8
df.resid 732 

Obviously the data is still overdispersed after the inclusion of a random effect. My question is: Should i use a GLM with quasibinomial? Or stay with glmer with the random effect? Or is there a better way to do it?

Also: I get this error returned when i try to run the glmer.

Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?

Is this because of the nature of my variables?


There's a lot on this in the relevant section of the GLMM FAQ: briefly, the three simplest approaches are to:

  • get the equivalent of a quasibinomial model by first fitting the model and adjusting the standard errors etc. post hoc (there's code on the GLMM FAQ to do this);
  • fit a compound model (Beta-binomial) — although you'll have to switch to glmmTMB or some other package to do it
  • add an observation-level random effect (technically, a "logit-Normal-binomial compound model")

As for the rescaling: hard to know without seeing your data, but guessing that your problem is either (1) you're treating Year as a numeric variable and haven't rescaled or centered it; or (2) you have complete separation.

Harrison, Xavier A. 2015. “A Comparison of Observation-Level Random Effect and Beta-Binomial Models for Modelling Overdispersion in Binomial Data in Ecology and Evolution.” PeerJ 3 (July): e1114. https://doi.org/10.7717/peerj.1114.

  • $\begingroup$ Thank you very much for your response, very clear and helpful. I now understand and have worked around the problem. $\endgroup$ – sinsam23 Jun 19 '20 at 16:04
  • $\begingroup$ OK: if this solves your problem you are encouraged to click the check-mark to accept the answer ... $\endgroup$ – Ben Bolker Jun 19 '20 at 17:32

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