I am running a fixed effects poisson model with robust standard errors in STATA (xtpqml). The model I run it on has my count data as dependent variable and then as my independent variable I have a damage index that is normalized to be between 0 and 1.
However, I wanted to check for non-linearities and split the damage index into two variables, one containing damage above a threshold (DH) and the other one under it (DL).
The results show that DL has a higher coefficient than DH, i.e. for each unit of damage, the effect is higher for the low damage group than for the high damage group.
Now intuitively I can see how that might be true, given that DL will have a much lower mean, so the overall effect of the low damage group is much smaller (when looking at means).
Is my intuition right? And if it is, why is it the case? Is it related to the variable being capped? Or is it the normalization?