interpret value errors for ordinal and categorical models

[GStechschulte]

interpret does not work with models (ordinal and categorical regression) whose predictions are a vector of some quantity, e.g., probabilities. This is because each value in the vector of probabilities is associated with a category / class. When the model's predictions are assigned to the summary dataframe, a value error is raised as the summary dataframe is expecting one prediction for each row.

For example:

length = [
    1.3, 1.32, 1.32, 1.4, 1.42, 1.42, 1.47, 1.47, 1.5, 1.52, 1.63, 1.65, 1.65, 1.65, 1.65,
    1.68, 1.7, 1.73, 1.78, 1.78, 1.8, 1.85, 1.93, 1.93, 1.98, 2.03, 2.03, 2.31, 2.36, 2.46,
    3.25, 3.28, 3.33, 3.56, 3.58, 3.66, 3.68, 3.71, 3.89, 1.24, 1.3, 1.45, 1.45, 1.55, 1.6,
    1.6, 1.65, 1.78, 1.78, 1.8, 1.88, 2.16, 2.26, 2.31, 2.36, 2.39, 2.41, 2.44, 2.56, 2.67,
    2.72, 2.79, 2.84
]
choice = [
    "I", "F", "F", "F", "I", "F", "I", "F", "I", "I", "I", "O", "O", "I", "F", "F",
    "I", "O", "F", "O", "F", "F", "I", "F", "I", "F", "F", "F", "F", "F", "O", "O",
    "F", "F", "F", "F", "O", "F", "F", "I", "I", "I", "O", "I", "I", "I", "F", "I",
    "O", "I", "I", "F", "F", "F", "F", "F", "F", "F", "O", "F", "I", "F", "F"
]

sex = ["Male"] * 32 + ["Female"] * 31
data = pd.DataFrame({"choice": choice, "length": length, "sex": sex})
data["choice"]  = pd.Categorical(
    data["choice"].map({"I": "Invertebrates", "F": "Fish", "O": "Other"}),
    ["Other", "Invertebrates", "Fish"],
    ordered=True
)

model = bmb.Model("choice ~ length + sex", data, family="categorical")
idata = model.fit(
    draws=1000, target_accept=0.95, random_seed=1234, chains=4
)

bmb.interpret.predictions(
    model=model,
    idata=idata,
    covariates="length"
)

ValueError: Expected a 1D array, got an array with shape (50, 3)

The ValueError is raised due to the 3 classes. For each sample in the new dataframe fed to the model, the model predicts a probability for each class. We could convert the xarray into a dataframe and perform a left join on this to ensure the data used to perform predictions is joined correctly with the predictions and uncertainty intervals.

In the example of bmb.interpret.predictions I envision the summary dataframe looking something like this

length	sex	choice_dim	estimate
1.240000	Male	Other	0.097136
1.240000	Male	Invertebrates	0.638881
1.240000	Male	Fish	0.263982
...	...	...	...
3.890000	Male	Other	0.316271
3.890000	Male	Invertebrates	0.002594
3.890000	Male	Fish	0.681135

where each row (sample) has been duplicated two times due to the left join. The user can now analyse the predicted probabilities for each class when length = 1.24 and sex = Male. This summary df would then be passed to the plot_predictions.