Data set with a distribution similar to Poisson, which regression to use?

Question

I am working on a research model looking at the data from stack overflow, especially the relationship of various variables on the score of a question. looking at the histogram of my dependent variable (Score) it holds a distribution similar to Poisson where most of the questions get a score of 0 or 1 and then a few questions get more upvotes while the histogram is right-skewed. The problematic part is that some questions get a negative score.

Looking at the data, I was quite convinced that the score is a count data. The values range from -12 to around 150.

I tested the model using glm in r

output <-glm(formula =  Score+12 ~ AnswerCount+AnswererRep+TimeDiff+AnswerQuotes, data = sds[[1]],
             family = poisson, )

output2 <-glm(formula =  Score+12 ~ AnswerCount+AnswererRep+TimeDiff+AnswerQuotes, data = sds[[1]],
             family = quasipoisson )

In addition the model reports underdisperssion (0.48) therefore I run a quasiposisson test. I tried a glm.nb (from MASS package) where the theta variable went up to > 40000. And r reported a warning message:

Warning messages:
1: In theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace = control$trace >  :
  iteration limit reached
2: In theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace = control$trace >  :
  iteration limit reached

In the end, I am just not sure what would be the correct regression model to use and whether the glm is the way to go. And if so, is it okay to add a constant (+12) to the dependent variable? Since I found some people be both for and against that.

Answer 1

Perhaps you can model it as a sum of upvotes and downvotes (counted negatively), both as a Poisson distribution. That would probably require counts of both as well. It would more naturally fit a Poisson distribution, where the rate is proportional to the fraction of visitors inclined to up- of downvote respectively.

If you don't have the up- and downvote counts separately, I don't really like the idea of adding 12 to all counts, but I don't have a better suggestion. Perhaps you have the number of views to work with? You could then model the score as the sum of a -1, 0, 1 variable (an ordinal) for each visitor.