My dependent variable contains positive integers truncated at 1. It is also quite skewed. The n is small with 48 observations. My first try was a multiplicative (log-log) model. Thinking I could improve on the Mean Squared Error, I tried quantile regression at the 25th percentile. This had the positive effect of reducing the MSE by 33% versus the OLS multiplicate model, but had the undesireable result of producing some negative predictions. So, I tried Proc QLIM specifying a truncated lower bound equal to 1, thinking that any predictions from this procedure would be constrained at the lower bound.
I was wrong. Proc QLIM produces negative predictions in spite of a lower bound at 1. This result is unexpected and surprising. The documentation doesn't address the issue.
What am I missing here?
