Return interpret data

[GStechschulte]

This PR addresses issue https://github.com/bambinos/bambi/issues/703 and #751 by adding a parameter return_idata: bool = False in comparisons(), predictions(), and slopes() that merges the posterior draws with the corresponding observation that "produced" that draw and returns it as a dataframe.

Most of the code diff is from adding a new test file that tests non-plotting functionality of the interpret sub-package not tested in test_plots.py.

fish_data = pd.read_stata("http://www.stata-press.com/data/r11/fish.dta")
cols = ["count", "livebait", "camper", "persons", "child"]
fish_data = fish_data[cols]
fish_data["livebait"] = pd.Categorical(fish_data["livebait"])
fish_data["camper"] = pd.Categorical(fish_data["camper"])

fish_model = bmb.Model(
    "count ~ livebait + camper + persons + child", 
    fish_data, 
    family='zero_inflated_poisson'
)

fish_idata = fish_model.fit(
    draws=1000, 
    target_accept=0.95, 
    random_seed=1234, 
    chains=4
)

With return_idata=True, one data frame is returned. This dataframe contains the inference data from the posterior groupInferenceData object, observed data, and parameter estimates. In the case that a user is calling predictions with pps=True, then the posterior predictive group is used. {marginaleffects} has a similar functionality for Bayesian models.

Below are a few examples:

bmb.interpret.predictions(
    model=fish_model,
    idata=fish_idata,
    conditional=["persons", "child", "livebait"],
    return_idata=True
) 

chain	draw	livebait_dim	camper_dim	Intercept	livebait	camper	persons	child	count_psi	count_mean	persons_obs	child_obs	livebait_obs	camper_obs
0	0	1.0	1.0	-2.560515	1.877271	0.658819	0.850313	-1.256469	0.619094	0.349454	1.0	0.0	0.0	1.0
0	1	1.0	1.0	-2.746079	1.852347	0.794963	0.848145	-1.302583	0.643842	0.331884	1.0	0.0	0.0	1.0
0	2	1.0	1.0	-2.669619	1.674642	0.693835	0.923590	-1.588417	0.683065	0.349171	1.0	0.0	0.0	1.0
0	3	1.0	1.0	-2.581749	1.474203	0.661846	0.958753	-1.624487	0.684139	0.382453	1.0	0.0	0.0	1.0
0	4	1.0	1.0	-2.866501	2.162873	0.575769	0.860328	-1.311473	0.647937	0.239212	1.0	0.0	0.0	1.0

1200000 rows × 15 columns

Returning the inference data when calling comparisons will allow the user to conduct more specific or complex comparisons leveraging group by aggregations:

bmb.interpret.comparisons(
    model=fish_model,
    idata=fish_idata,
    contrast={"persons": [1, 4]},
    conditional={"child": [0, 1, 2], "livebait": [0, 1]},
    return_idata=True
) 

chain	draw	livebait_dim	camper_dim	Intercept	livebait	camper	persons	child	count_psi	count_mean	child_obs	livebait_obs	persons_obs	camper_obs
0	0	1.0	1.0	-2.560515	1.877271	0.658819	0.850313	-1.256469	0.619094	0.349454	0.0	0	1.0	1.0
0	1	1.0	1.0	-2.746079	1.852347	0.794963	0.848145	-1.302583	0.643842	0.331884	0.0	0	1.0	1.0
0	2	1.0	1.0	-2.669619	1.674642	0.693835	0.923590	-1.588417	0.683065	0.349171	0.0	0	1.0	1.0
0	3	1.0	1.0	-2.581749	1.474203	0.661846	0.958753	-1.624487	0.684139	0.382453	0.0	0	1.0	1.0
0	4	1.0	1.0	-2.866501	2.162873	0.575769	0.860328	-1.311473	0.647937	0.239212	0.0	0	1.0	1.0

48000 rows × 15 columns

Initially, I wanted to return the az.InferenceData object. However, due to the following limitations I settled on a DataFrame:

• I could add new groups to the inference data object, but then it isn't clear to me how to perform group by aggregations on the posterior dataset while taking into account this new group.

• Additionally, the data shouldn't be merged as a data variable in the az.InferenceData.posterior dataset because, when aggregations are performed along the coordinates, these aggregations will also be applied to the data used to generate the predictions (since they were merged as a data variable).

• Lastly, the data could be merged and made as a coordinate so you can specify along which dimension(s) you want to compute the aggregation. Although, I can't seem to groupby more than one coordinate. For example, xr.Dataset.groupby([coord1, coord2]) results in the following error:

TypeError: group must be an xarray.DataArray or the name of an xarray variable or dimension. Received ['coord1', 'coord2'] instead.

Note: depending on the model specification and number of chains and draws, it is possible there will be millions of rows returned.

To do:

• [x] add case for when pps=True (posterior predictive samples) in predictions. Currently, I only access the posterior group of the InferenceData to build the dataframe.

[codecov-commenter]

Codecov Report

Attention: 1 lines in your changes are missing coverage. Please review.

Comparison is base (dcd879b) 89.90% compared to head (6208fe8) 89.91%.

Files	Patch %	Lines
bambi/interpret/utils.py	90.00%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #758 +/- ## ========================================== + Coverage 89.90% 89.91% +0.01% ========================================== Files 45 45 Lines 3713 3729 +16 ========================================== + Hits 3338 3353 +15 - Misses 375 376 +1 ```

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[GStechschulte]

Thanks for the nice feature! Just a couple of suggestions.

Thanks for the review. I will incorporate these once we finalize the implementation per our conversation on Slack.

[GStechschulte]

Closing in favor of #762