I need to do a regression on a variable Y that is skewed right (non normal) and heteroskedastic and therefore violates two assumptions of the normal linear model. The data is non negative (some 0 values) and discrete.
As you can see, it is a count variable but it has a very wide range (it counts minutes in increments of ten), which is why I initially excluded a Poisson regression as I thought that given the high counts it would approx a normal distribution (even dividing by ten and the maximum value is 175).
Now, I have 2 doubts:
- I had to translate the data to use the boxcox function in R because of the 0 values, so I don't know if, when I apply the linear model to the square root of Y, I should use the translated or original data set (it gives me a difference in significance for some regressors).
- Even using a square root instead of the regular box cox transformation, the interpretation is not as straightforward as I would like (in terms of the explanation of the phenomenon, not just how I would interpret the parameters).
So I was thinking of possibly using a GLM with a Gamma distribution instead of Poisson, but I am not sure if it makes sense with the data I have (discrete and with some 0 values). I am not super familiar with the model so I am unsure, but it is appealing to me as it might have a more useful interpretaion b/c of the multiplicative structure?
Considering all of this, which model is better suited? Should I stick with box-cox or use Poisson or Gamma?
I should note that in the original linear model I had a couple of interactions, so I am not sure it would work with the glms.
Thank you, sorry if my summary was too confused, I have not applied a lot of statistical models to real world data :)