Poisson regression: an offset variable with values of ZERO

[joe cai]

Hi all,

I got a question: I am using a "ppmlhdfe" command for a Poisson regression with log offset "exp" options to estimate a rate (it's number of citations per patent). So the option is: xxxxxx, exp(patent number). However, some firms have zero patent. In this case, how can I deal with the issue? Thank you very much.

Joe

[Leonardo Guizzetti]

An exposure (or the log of exposure, called an offset), is a way to allow for the regression to estimate an incidence density (e.g., per unit time or area). It must be a value greater than 0, because the log of non-positive values is undefined, and further, using a non-positive value in the denominator is non-sense and cannot be interpreted.

I'm not an economist, but what use can firms with no patients be if your interest is in estimating citation rates per patent? You would effectively be trying to divide by zero. You may consider only modeling firms that have patents and ignoring those that don't.

[joe cai]

Thank you, Leo. Let me think about it and see whether I really want it.

[Dart Stater]

Can be exposure or offset variable used for background risk modelling? For example, we have age at exposure and sex, as a background risk factors, and the dose to estimate the excess mortality risk.

[Leonardo Guizzetti]

No. Exposure is a more technical aspect of GLMs and is best thought of as the denominator to a risk or a rate (e.g., time, person-time, total counts).

[Dart Stater]

Leonardo, thank you for the answer!
As I understand, the exposure variable should be a linear predictor. As it was discussed here https://www.statalist.org/forums/for...le#post1417565 the fleet size can serve as exposure assuming that more vehicles produce more accidents. But what if our exposure variable (or that we want to use as exposure) has non-linear form? The hypothesis is that at certain time really big fleet size to support the brand hires more experienced drivers resulting in declining the rate of accidents compared to the fleet that is big but not a brand yet.
In that situation we sholuld expect a linear - quadratic relationship between exposure var and the outcome. How to create an exposure in this case?

[Leonardo Guizzetti]

In those cases you simply enter them like any other predictor in the model with whatever transformation makes sense (e.g., quadratic and linear terms). The only special aspect of the exposure variable is that the coefficient is fixed at 1. If this isn’t required, then it is like any other predictor.