confidence and prediction intervals with StatsModels

Question

I do this linear regression with StatsModels:

import numpy as np import statsmodels.api as sm from statsmodels.sandbox.regression.predstd import wls_prediction_std  n = 100  x = np.linspace(0, 10, n) e = np.random.normal(size=n) y = 1 + 0.5*x + 2*e X = sm.add_constant(x)  re = sm.OLS(y, X).fit() print(re.summary())  prstd, iv_l, iv_u = wls_prediction_std(re) 

My questions are, iv_l and iv_u are the upper and lower confidence intervals or prediction intervals?

How I get others?

I need the confidence and prediction intervals for all points, to do a plot.

Answer 1

For test data you can try to use the following.

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

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.

I am posting this here because this was the first post that comes up when looking for a solution for confidence & prediction intervals – even though this concerns itself with test data rather.

Here's a function to take a model, new data, and an arbitrary quantile, using this approach:

def ols_quantile(m, X, q):   # m: OLS model.   # X: X matrix.   # q: Quantile.   #   # Set alpha based on q.   a = q * 2   if q > 0.5:     a = 2 * (1 - q)   predictions = m.get_prediction(X)   frame = predictions.summary_frame(alpha=a)   if q > 0.5:     return frame.obs_ci_upper   return frame.obs_ci_lower 

Answer 2

update see the second answer which is more recent. Some of the models and results classes have now a get_prediction method that provides additional information including prediction intervals and/or confidence intervals for the predicted mean.

old answer:

iv_l and iv_u give you the limits of the prediction interval for each point.

Prediction interval is the confidence interval for an observation and includes the estimate of the error.

I think, confidence interval for the mean prediction is not yet available in statsmodels. (Actually, the confidence interval for the fitted values is hiding inside the summary_table of influence_outlier, but I need to verify this.)

Proper prediction methods for statsmodels are on the TODO list.

Addition

Confidence intervals are there for OLS but the access is a bit clumsy.

To be included after running your script:

from statsmodels.stats.outliers_influence import summary_table  st, data, ss2 = summary_table(re, alpha=0.05)  fittedvalues = data[:, 2] predict_mean_se  = data[:, 3] predict_mean_ci_low, predict_mean_ci_upp = data[:, 4:6].T predict_ci_low, predict_ci_upp = data[:, 6:8].T  # Check we got the right things print np.max(np.abs(re.fittedvalues - fittedvalues)) print np.max(np.abs(iv_l - predict_ci_low)) print np.max(np.abs(iv_u - predict_ci_upp))  plt.plot(x, y, 'o') plt.plot(x, fittedvalues, '-', lw=2) plt.plot(x, predict_ci_low, 'r--', lw=2) plt.plot(x, predict_ci_upp, 'r--', lw=2) plt.plot(x, predict_mean_ci_low, 'r--', lw=2) plt.plot(x, predict_mean_ci_upp, 'r--', lw=2) plt.show() 

This should give the same results as SAS, http://jpktd.blogspot.ca/2012/01/nice-thing-about-seeing-zeros.html