estimate_dispersion() (and maybe estimate_zeroinflation()?)

[bwiernik]

For models with dispersion models, it would be nice if two things were possible:

1. Incorporation of modeled dispersion parameters into prediction intervals in estimate_prediction().
2. Estimate predicted dispersion and confidence intervals on the link or response scale. This could be an option in estimate_response() and related functions (cf. get_predicted(): zero-inflation options insight#413) or a separate estimate_dispersion(). Like with estimate_prediction(), making this an alias of estimate_response() with default options might make sense.

Relatedly, options for estimating zero-inflation predictions would be great.

[bwiernik]

What do you think about API here? @DominiqueMakowski

[strengejacke]

We could add this easily, simply by calling estimate_means() with the appropriate type argument. So these functions could simply be wrappers.

[DominiqueMakowski]

I have little experience with ZI-like models to be honest, so I'll defer judgment here. If I understand, we are talking about two things:

1. Integrate more-or-less sources of variances (random effects, ZI, etc) into predictions/means/ etc.: this should probably be done through arguments
2. Predict the value of specific parameters (instead of the expected outcome value). This mostly applies for non-linear models, where we can have more than a couple parameters estimated (which I commonly use in brms). For this, maybe introducing a new estimate_parameter(model, which="sigma", by="var1") would make sense? This could also be used to predict the ZI parameter

does that make sense?

[strengejacke]

I just saw that my comment was only addressing the 2nd point. Brenton was talking about incorporating uncertainty into intervals in his 1. point.

[strengejacke]

does that make sense?

Yes, sounds good. We could still use estimate_means() internally to get predictions for the different parameters, which is usually changed via the type argument. See, e.g., #278 where the ZI probabilities are predicted.