# intepreting Negative coefficients of Poisson model [duplicate]

i have fitted a Poisson regression to my claim frequency data. my predictor is make of vehicle.

I have obtained the following result:

Coefficients:
Estimate  Std. Error  z value Pr(>|z|)
(Intercept)  -19.99774  1138.82118  -0.018  0.98599
make2         -0.30873    0.20550  -1.502   0.13302
make3         -0.39177    0.21129  -1.854   0.06372
make4         -0.38375    0.13388  -2.866   0.00415 **


How do I interpret the negative coefficients? Thanks

## marked as duplicate by COOLSerdash, user88 Feb 23 '14 at 11:30

• You don't mention a link function, which matters for interpretation. From the look of it, I assume it was a log-link. Is that the case? Is make a straight categorical variable - a factor - from which we can take these coefficients to be those going with 0-1 dummies? – Glen_b Feb 23 '14 at 6:09
• On reflection, I am curious to know how you'd interpret positive coefficients in this model, if you had them. I suspect, if negative coefficients are giving you a problem, your notion of the meaning of the positive ones is probably incorrect. – Glen_b Feb 23 '14 at 6:37
• Is this for some subject? – Glen_b Feb 23 '14 at 9:30
• It's kind of amusing that the supposed duplicate was answered by me and I don't think it's a duplicate. Not every question about interpretation has the same answer. I nominated the question for reopening so that perhaps further commentary could be placed on the proper handling of pathological data situations that doe not throw obvious error messages. – DWin Feb 23 '14 at 16:28

The large standard error and the rather large Intercept estimate are a sign of model failure. You have complete separation or some other pathological situation. The Poisson models are constructed on a log scale so the intercept is estimated at a value on the native scale that R reports as effectively zero: exp(-19) returns 5.602796e-09. So I think you need to look at tabular cuts of your data before you worry about what to do with those coefficients.

You probably have zero events in the make==1 level of a factor. The other factor levels are reference to the base level, so it's not going to make much sense to make small ratio adjustments to an estimate of zero.

• Your discussion of how to convert the intercept to the "native scale" is wrong. It doesn't involve taking the log of the intercept. – Glen_b Feb 23 '14 at 9:27
• (Apologies for taking the log when I should have been exponentiating. But it doesn't change the fact that there is a pathological data problem.) – DWin Feb 23 '14 at 16:26
• I have removed a predictor which was causing the high standard error. However i am still left with a residual deviance of 627. Should that be a matter of concern? Thanks @ DWin – user40494 Feb 23 '14 at 16:36
• The residual deviance alone is not adequate for judging model adequacy. It can be affected by extraneous issues like whether the data was aggregated or single subject per line. And whether removing that factor was the right thing to do is not yet clear. The process of understanding relationships starts with the scientific question and then moves on to tabular views of the data and only then you are ready for the modeling stage. I fear you are short-circuiting the process. – DWin Feb 23 '14 at 17:49