Let `Fepois` inherit from `Feglm`?

[leostimpfle]

Feglm implements the iterative weighted least squares algorithm by Stammann (2018) in Feglm.get_fit. While this method also works for Poisson regressions, there is currently a separate Fepois.get_fit.

I guess this is historically grown because we first had Poisson regressions and only recently implemented GLMs, but I had two questions:

• Are Feglm.get_fit and Fepois.get_fit in fact equivalent?
• Would it make sense to make Fepois inherit from Feglm (similarly to Felogit etc)?

I believe that in fixest Poisson is just another GLM "family" but follows the same structure and uses the same methods as other GLM families.

[leostimpfle]

The discussion in #668 is relevant

[s3alfisc]

In general, I believe this makes sense. But would like to discuss this more throughly before we start:

• should we implement fixed effects support for the other GLMs first?
• should we do an even larger refactor and create a BaseRegression class that all classes, including Feols, inherit from?

[leostimpfle]

Yes to both, this is probably more a medium term problem to tackle.

Specifically, I think it makes sense to first add fixed effects to GLMs #872 (and also fix prediction for Poisson with fixed effects and newdata #468 which I'm working on currently).

I also think that having a BaseRegression class is a good idea. For example, Fepois.predict currently calls Feols.predict which itself calls some methods that do not allow passing a prediction type, i.e., "response" or "link", likely because it's the same for OLS (but not for Poisson). Having Fepois not inherit from Feols would help us separate concerns more clearly.