Add methods like `logLik()` etc. for *multinom_weightit* and *ordinal_weightit*?

[strengejacke]

We started implementing support the WeightIt package in our easystats-eco-system, mainly in insight (https://cran.r-project.org/package=insight) and parameters (https://cran.r-project.org/package=parameters, update to be submitted).

I'd also like to provide support in the performance package (https://cran.r-project.org/package=performance). While this works well for glm_weightit(), the multinom and ordinal regressions don't provide methods like logLik() or AIC() etc. Do you plan to add those methods to the models, too?

Another question would be how the weighting affects R2 measures - if the log-lik is available for, say, multinom, can you use the same pseudo R2 measures (Nagelkerke, Cox & Snell) for multinom_weightit or is it more complicated?

[ngreifer]

Hi Daniel,

Thanks for adding support for WeightIt's modeling functions! I'll look into adding logLik() and related methods. The reason I didn't implement them already is that I don't know exactly how likelihoods and related statistics are computed when the model is weighted. I wanted to discourage users from doing LR tests or comparing models based on AIC/BIC because I'm not sure that they work with weighted models. Of course, these functions support unweighted models, too, and there is no reason to omit these functions for such cases. Also, the models are fit using weighted MLE, so it is definitely possible to compute a weighted likelihood. I also wanted these models to be primarily used for outcome models in the context of causal effect estimation rather than general modeling functions, so I wasn't too concerned with providing statistics that summarize the whole model beyond the treatment effect. See #59 for my reasoning.

I'll work on this in the next few weeks. If you find any interesting resources that explain these issues, I would appreciate that. I think functions in the survey package have similar challenges, so I'll read up more on how those are addressed. I don't think the same amount of research has gone into PS-weighted models, though.

Noah