[jonathan-taylor]

The response of a model, and R's ., for 0.2.0.

Responses. ModelSpec(terms, response=...) and spec.build_response(X) build the response from the same data as the design. A response can be:

• a column, or a list of columns;
• Surv(time, status) / Surv(start, stop, status), as R's (keywords stop=, status=, start= also work). Returns a pd.DataFrame of those columns, named as in X: what glmstar's CoxFamily(event_id=..., status_id=..., start_id=...) and lifelines take;
• Binomial('y') for a binary column: 0/1, boolean, or two levels, with the second level (as in R) or level= counted as a success. Binomial(successes, trials=...) gives either successes and failures (output='counts', R's cbind, which statsmodels' GLM takes) or the proportion and the number of trials (output='proportion': a response and its weights, e.g. for glmstar);
• Multinomial('class') for the class of each row, as a categorical with the levels seen at fit or one-hot (output='onehot'). Multinomial([...]) takes counts.

Responses learn their levels at fit, and a level unseen at fit raises. The response's columns cannot be used in a term. The response objects are fit as copies, so response is never modified.

The method is build_response, not response, because response is the parameter's name (sklearn stores parameters as attributes). The name also parallels build_submodel and build_sequence.

wildcard, an object rather than the string '.'. It stands for every column of X except the response, and is expanded at fit into expanded_terms_; terms is unchanged.

• MS([wildcard], response='y') is y ~ .
• wildcard(pow=2) is .^2, and wildcard(exclude=['x']) is . - x
• (wildcard, 'g') is .:g
• pca(wildcard, n_components=3) is a feature built from every column. It can be tuned with terms__0__n_components, and pca()'s name is now optional.

As in R's y ~ x + ., columns (and interactions, in any order) that are already terms are not repeated. pow > 1 is only allowed when the wildcard is itself a term.

fit(X, y) checks that the indices agree when both are pandas objects.

Tests: tests/test_wildcard.py and tests/test_response.py. They check against statsmodels: PHReg on Surv, and binomial GLM with counts versus proportion plus var_weights. The full suite gives 261 passed and 5 strict xfails, and the new tests also pass with warnings as errors.

Docs: a "Responses and the wildcard" page, executed locally with Jupyter Book 2. Sales ~ . gives the same OLS coefficients as R's lm(Sales ~ ., Carseats). The API reference gains the new classes.

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