ENH: postestimation for ANCOVA type regression models, predicted means

[josef-pkt]

this is an integration issue to bring different things together for one type of analysis.

The model is as in ANCOVA with one or several factor variables and their interactions and some continuous (confounder or control) variables.

We need hypothesis tests, prediction, plots and "post-hoc" analysis (like pairwise comparisons)
We have many of those already but not applicable or specialized for this use case.

several of those tasks should be beginner friendly, for example the plots.

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example pairwise comparison after OLS or GLM similar to tukeyhsd

My initial plan was to recover the contrast matrices for the restrictions based on the estimated parameters and the encoding used in the creation of the factor/dummy columns in the design matrix.

Nathaniel's idea (discussed with him at pycon) was to use prediction to get the relevant means and contrasts. This has the advantage that by going through patsy, the prediction is independent of the actual encoding of the factor. The main problem is that, in order to call the design matrix for new values of the exog, we need to have enough information to create them in the same ways as they were defined in the original data of the user (i.e. exog_orig)