I have under-dispersed count data. I do not want to transform them, and using a negative binomial error distribution (via glmer.nb) does not help.
My results are the same regardless of the distribution I use, and agree very well with the conclusion that you would draw by eyeballing the data (it is pretty obvious that there is no effect, see below). I can not seem to find any real way to deal with this problem, and I am left wondering if the most appropriate thing to do is acknowledge the under-dispersion, point to the result that is robust to every method I've thrown at it, and move on.
If you've been in this situation- could you share any tools/advice/philosophy that you found helpful?
Here is the output from my Poisson model:
mc_p<-glmer(tubes ~ status + (1|site/plant), family="poisson", data=mc) summary(mc_p) Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod'] Family: poisson ( log ) Formula: tubes ~ status + (1 | site/plant) Data: mc
AIC BIC logLik deviance df.resid 713.7 725.7 -352.8 705.7 143 Scaled residuals: Min 1Q Median 3Q Max -2.08950 -0.38627 -0.04237 0.33830 2.87921 Random effects: Groups Name Variance Std.Dev. plant:site (Intercept) 0.01958 0.1399 site (Intercept) 0.01790 0.1338 Number of obs: 147, groups: plant:site, 20; site, 4 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 2.25665 0.08417 26.809 <2e-16 *** statusy 0.01356 0.05301 0.256 0.798 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) statusy -0.308
I am trying determine whether pollen tube counts differ between nectar-robbed and un-robbed flowers. Pollen tube counts are nested within plant (multiple flowers of each type sampled from each plant) and plants are nested within site. I've tried using a negative binomial error distribution (as I described in the first iteration of this post), but that still gave me a very high deviance relative to my residual df. It seems that there isn't a straight-forward way to apply a useful error distribution to my nested data. At the same time, the result (that there is no difference between groups) is the same regardless of how I arrange my model, and can be seen very clearly in the bar-graph above.