I learned about the zero-inflated negative binomial distribution a few months ago when I was trying to do regression on some discrete data. I have a different data set now, and it seems to be very similar except that the value 1
seems to be over-represented (as opposed to 0
). Is there such a thing as a one-inflated negative binomial distribution? How could I model these data?
1 Answer
Sure. You can write
$Pr(X=x) = p*f(x) + (1-p)1(x=1)$
where $f$ is the NB pmf, $1()$ is just an indicator function and $p$ is some probability. Of course in general the $x=1$ could be $x=k$ for any integer $k$, and $f$ could be any pmf.
In principle it shouldn't be harder to fit than a ZI model, but an off-the-shelf model-fitting solution may not exist.
1
, make sure that there is a logical reason for the1
s to be over-represented. When you figure out why are there too many1
s, you might find the most appropriate model. $\endgroup$1
value is significantly over-represented because it is the minimum value representing the simplest case for the data I am measuring. I guess I could transform the data (x' = x-1) and then use the zero-inflated model, but I wasn't sure what effect that would have and if the interpretation of the results would be the same. $\endgroup$