Return std and confidence intervals for out-of-sample prediction in StatsModels

Question

I'd like to find the standard deviation and confidence intervals for an out-of-sample prediction from an OLS model.

This question is similar to Confidence intervals for model prediction, but with an explicit focus on using out-of-sample data.

The idea would be for a function along the lines of wls_prediction_std(lm, data_to_use_for_prediction=out_of_sample_df), that returns the prstd, iv_l, iv_u for that out of sample dataframe.

For instance:

import pandas as pd
import random
import statsmodels.formula.api as smf
from statsmodels.sandbox.regression.predstd import wls_prediction_std

df = pd.DataFrame({"y":[x for x in range(10)],
                   "x1":[(x*5 + random.random() * 2) for x in range(10)],
                    "x2":[(x*2.1 + random.random()) for x in range(10)]})

out_of_sample_df = pd.DataFrame({"x1":[(x*3 + random.random() * 2) for x in range(10)],
                                 "x2":[(x + random.random()) for x in range(10)]})

formula_string = "y ~ x1 + x2"
lm = smf.ols(formula=formula_string, data=df).fit()

# Prediction works fine:
print(lm.predict(out_of_sample_df))

# I can also get std and CI for in-sample data:
prstd, iv_l, iv_u = wls_prediction_std(lm)
print(prstd)

# I cannot figure out how to get std and CI for out-of-sample data:
try:
    print(wls_prediction_std(lm, exog= out_of_sample_df))
except ValueError as e:
    print(str(e))
    #returns "ValueError: wrong shape of exog"

# trying to concatenate the DFs:
df_both = pd.concat([df, out_of_sample_df],
                    ignore_index = True)

# Only returns results for the data from df, not from out_of_sample_df
lm2 = smf.ols(formula=formula_string, data=df_both).fit()
prstd2, iv_l2, iv_u2 = wls_prediction_std(lm2)
print(prstd2)

Answer 1

It looks like the problem is in the format of the exog parameter. This method is 100% stolen from this workaround by github user thatneat. It is necessary because of this bug.

def transform_exog_to_model(fit, exog):
    transform=True
    self=fit

    # The following is lifted straight from statsmodels.base.model.Results.predict()
    if transform and hasattr(self.model, 'formula') and exog is not None:
        from patsy import dmatrix
        exog = dmatrix(self.model.data.orig_exog.design_info.builder,
                       exog)

    if exog is not None:
        exog = np.asarray(exog)
        if exog.ndim == 1 and (self.model.exog.ndim == 1 or
                               self.model.exog.shape[1] == 1):
            exog = exog[:, None]
        exog = np.atleast_2d(exog)  # needed in count model shape[1]

    # end lifted code
    return exog

transformed_exog = transform_exog_to_model(lm, out_of_sample_df)
print(transformed_exog)
prstd2, iv_l2, iv_u2 = wls_prediction_std(lm, transformed_exog, weights=[1])
print(prstd2)

Answer 2

Additionally you can try to use the get_prediction method.

predictions = result.get_prediction(out_of_sample_df)
predictions.summary_frame(alpha=0.05)

This returns the confidence and prediction interval. I found the summary_frame() method buried here and you can find the get_prediction() method here. You can change the significance level of the confidence interval and prediction interval by modifying the "alpha" parameter.