How to specify offset in poisson regression?

Questions
1

Hi,

Using the glm module, how can I build a poisson regression model that features an offset variable with a parameter estimate constrained to 1? In R, one would use the offset function:

glm(y ~ offset(log(exposure)) + x, family=poisson(link=log) )

Thanks,
Fabian

2

The glm-module uses patsy for the formulas, and as far as I know that doesn’t have support for offsets. You’ll have to set up the model manually without the glm module:

with pm.Model() as model:
    ...
    beta = pm.Flat('beta')  # Or whatever is appropriate for your model
    predictor = tt.log(exposure) + beta * x
    pm.Poisson('y', mu=tt.log(predictor), observed=data)
3

OK - thanks. I assume you mean to use the exp function when specifying mu, i.e.:

with pm.Model() as model:
    ...
    beta = pm.Flat('beta')  # Or whatever is appropriate for your model
    predictor = beta * x
    pm.Poisson('y', mu=exposure * tt.exp(predictor), observed=data)```
4

You are right of course, it is tt.exp.