ENH/Design: diagnostics based on linear predictor or tranformed distribution

[josef-pkt]

Just an idea: For some models with might want to have diagnostics based on linear predictor or transformed distribution.

example:
accelerated failure time model and log-transformed distribution
Compute diagnostic for the normal model instead the log-normal model.
The log-normal model does not have a mean parameterization and it will be easier to use the diagnostic of the log transformed model, e.g. the normal model instead directly in the log-normal model.

Idea triggered by Inheritance of generically implemented features is great.
e.g. resid_pearson requires resid_response and predict "var". #7973 (comment)
We will get this only with difficulty in some models like log-normal and other variance/precision parameterized models like AFT.

Using diagnostics for linear predictor requires that we have an observable statistic to compare it with, eg. working residuals in GLM. (We don't do much with those currently,)
But traditional GLM influence-outlier analysis and diagnostic is mostly based on WLS/IRLS

Even if we use the transformed model for diagnostics, we still want the main model for the application specific parts, e.g. survival probabilities and quantiles.
And we can still do diagnostics other than residual diagnostics for those, e.g. quantile, gof based diagnostics.

unlikely for 0.14, unless we have diagnostics that we can just wire into those models. eg. GaussianHet diagnostics for log-normal.