Residuals of GAM models not improving with poisson or ziplss, but better with negative binomial (help with high values) I am running GAM models on species counts with lots of zeros and high values or high counts. Residuals under poisson family have a s-like curve on qq line with models not predicting lower and higher values well (see c. bottom figure). Residuals under negative binomial are better and appear more normal for the lower and middle values, while extreme values are off the qq line (see see a. top figure. I thought ziplss() might help normalize the residuals on the qq line, but low and high values are mapping off the qq line (s-like curve and wiggly, see b. middle figure) similar to the residuals for poisson. There are a few predictors that are factors in the dataset assigned as bs="re". The other predictors are continuous and assigned a bs="cr". Species counts are not log transformed, kept as counts. What could be the culprit? How to address this?




You could try a zero-inflated negative binomial, ZINBI,
or zero-adjusted negative binomial, ZANBI,
distributions available in the gamlss R package.
There are also heavier tailed and more flexible distributions available in gamlss:
ZIPIG, ZAPIG, (where PIG=Poisson Inverses Gaussian)
ZIBNB, ZABNB, (where BNB=beta negative binomial)
ZISICHEL, ZASICHEL, (where SICHEL=Sichel distribution).
