Offset in Logistic regression: what are the typical use cases?

Offset is commonly used in Poisson regression to take into account different exposure (different time periods for instance): offset = log of exposure

Question: what's the typical use case of offset in logistic regression?

I assume we can't do exposure (proportional effect) in classification problems since E(y|x) can't go beyond 1 so I'm curious about why someone would need to use offset in a logisic regression.

• Why "use cases" and not "examples"? – Frank Harrell Apr 8 '17 at 15:14

2 Answers

You include an offset when you know what the coefficient of that variable should be. Typically software fixes it at unity. As you point out in Poisson regression this is often used to include the effect of the denominator when we assume that if we multiplied the denominator by a factor we would also multiply the outcome by the same factor.

One case where an offset might be used outside the Poisson special case is when you have a hypothesised value for the coefficient from theory of previous studies. If you then include your predictor variable in the regression multiplied by the theoretical value and as an offset this will have the effect of including it with the theoretical value of the coefficient. If you also include the predictor as a standard regressor you will see from testing its coefficient against zero whether the offset is sufficient (so the theoretical value is supported) or whether you can reject that.

I sometimes use an offset in a logistic regression model. The use case is where I already have a complex model, which needs to be re-estimated to cover some new data outside the realm of the original data sample (in time, or in cross section), but where, for various reasons, it is practically infeasible to re-estimate the model on the entire, expanded data set. The goal is a new model that gives good predictions on some out-of-sample data, but which gives unchanged predictions on the in-sample data.

So I take the linear predictors from the original model, specify those as an offset, and then introduce additional variables aimed at fitting the new data, in such a way that it wouldn't change the predictions on the original data.

It's admittedly ad hoc, but an awfully useful trick in practice. I have no idea what the "legitimate" use of an offset in logistic regression is, but I'm glad statistical software packages allow for it.