I am running a negative binomial regression. One of my independent variables is a measure of distance traveled - half of the observations are 0 because they do not travel, while the other half have a non-zero, positive value equal to the distance they travel.
What is the best way to include such a variable in a regression? I suspect that having 50% 0s in the independent variable makes it difficult if not wrong to interpret the coefficient if the variable is included as is. On the other hand, a simple dummy variable could fix the problem, but then measuring the effect of each unit of distance traveled would not be possible.
Is separating the observations into a 0 and non-0 group a legitimate solution? Such that the same regression is applied in both cases, except the non-0 group is applied the distance traveled variable which now would have no 0s.
I am especially concerned because the variable is still significant (p<0.05) besides this less-than-convincing negative, linear relationship. There appear to be 11 of 550 (2%) observations that are outliers (those above DIST of 8). Common sense is telling me to throw this variable out - is having 11 outliers like this acceptable?