I am running some analyses on count data, and I am including a single random factor, thus I am using GLMM in r (glmer fo the package lme4).
In order to chose the best model and distribution I am running the same model with negative binomial distribution (glmer.nb) but also with a poisson distribution (glmer with family = poisson). Then I compare the residuals between the two models. However, in general, the negative binomial models show better fit, but they also give me a singularity warning when I ran them. I have tried simplifying the models, but I keep getting the singularity warning.
My question is: should I reject the singular model as invalid, even though ids the one with the best fit?
Cheers,
Miguel
I believe that the singularity simply means that the model cannot converge possibly because it tends to infinity. But that is a numerical problem with the computer's optimization and does not mean in any way that the model is good. If the data are such that some division is essentially zero in the denominator then the calculations could blow up to a seeming singularity.
Try it as not random effects and see what you get, equivalently constrain the level 2 random variance to zero, I am interested if there is any problem with the predictors, eg colinearity.
Instead of rejecting the model due to singularity, its better to change the method of parameter estimation while fitting the models using R for both models. By doing this singularity issue would be solved!
There is the bayesian method which can overcome this problem like bglm or bglmer in R
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