Using GLM: Gaussian, Poisson vs Gamma I am trying to perform a GLM analaysis using R for an outcome that is:

*

*Bounded by 0 - 10

*In steps of 1

(Numerical Rating Scale for Pain: 0 - 10)
I have a set of demographic factors, age, sex etc, that I want to input as factors for the GLM.
I understand that Gaussian might not be the best option (since bounded by 0) but am not sure if I should choose Gamma (since this is not continuous) or Poisson (since the outcome is not counts)
the data is very much skewed:

thanks
s

I would use logit  link and binomial family, without too much queasiness.
There will be, or should be, switches in your software to indicate bounds of 0 and 10, or more generally to work with the kind of data You are using R, but I won't attempt even broad coding advice.
I support what I take to be a widespread view that getting the link right (here to respect the bounded nature of the outcome) is more crucial than whichever family you specify. There is always small print about which choices give best guesses at standard errors and P-values.
In practice, you may get very similar predicted values  even with gamma and Poisson families, but the inferential details could vary quite a lot.  But watch out: with some choices you might get absurd negative predictions for your outcome, given a marginal distribution like that.
In sum: you're focusing on which error family to specify, but the link function is the first choice to make.
On a different level: this could be very awkward data for other reasons, depending on how far people reporting no pain could be qualitatively as well quantitatively different.
