Is your feature request related to a problem? Please describe

Post model training, it is helpful to know which variable was used as the offset. This aids in post model analysis and deployment.

The offset array is saved and can be accessed after saving the model, but the name of the offset variable is lost when it is a pandas series. The series is converted to a np.array which removed the name. Current state, it is difficult to tell which variable may have been used as an offset without tracking it outside the model.

Example use case: Sharing a saved model with a peer. They inspect it to determine what variable was used as the offset in training.

The same may apply to the var_weights and freq_weights for GLM.

Describe the solution you'd like

The model has access on __init__ to the name of the offset if it is a pandas series. A way to save the offset array's name if it is a series would be wonderful.

Similar to how the endog and exog names can be used in the model summary.

Here's a few ideas I had for how to implement this. Happy to hear if there's a better option.

1. Add an offset_name property for GLM
   • Similar to the base models endog_names/exog_names
   • Simple to implement
2. Add it to the model.data so it's handled by PandasData
   • The name could be added back to the offset when making the results wrapper (at least I think that's how it works)
   • I could use some guidance on how to implement this if it is the preferred approach
   • I think it has something to do with the data attrs but it's a bit hard to track down
3. Do not convert to a numpy array if it is a series
   • One could use model.offset.name to get at the variable name
   • Doesn't line up with how the rest of the code works, it expects numpy arrays
   • Likely not a good option
4. User adds offset_name attribute to the model class before saving it.
   • Seems like a bad idea, would like support in statsmodels

Describe alternatives you have considered

Current workaround is saving the offset name in a separate file, which is not ideal.

Additional context

Happy to work on a PR for this.