Python Statsmodels QuantReg Intercept

Question

Problem Setup In statsmodels Quantile Regression problem, their Least Absolute Deviation summary output shows the Intercept. In that example, they are using a formula

from __future__ import print_function
import patsy
import numpy as np
import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf
import matplotlib.pyplot as plt
from statsmodels.regression.quantile_regression import QuantReg

data = sm.datasets.engel.load_pandas().data

mod = smf.quantreg('foodexp ~ income', data)
res = mod.fit(q=.5)
print(res.summary())

                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                foodexp   Pseudo R-squared:               0.6206
Model:                       QuantReg   Bandwidth:                       64.51
Method:                 Least Squares   Sparsity:                        209.3
Date:                Fri, 09 Oct 2015   No. Observations:                  235
Time:                        15:44:23   Df Residuals:                      233
                                        Df Model:                            1
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept     81.4823     14.634      5.568      0.000        52.649   110.315
income         0.5602      0.013     42.516      0.000         0.534     0.586
==============================================================================

The condition number is large, 2.38e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

The Question

How can I achieve a summary output with the Intercept without using the statsmodels.formula.api as smf formula approach?

Launder

Answer 1

Of course, as I put this question together, I figured it out. Rather than delete it, I'll share in case somebody out there ever runs across this.

As I suspected, I needed to add_constant() but I wasn't sure how. I was doing something dumb and adding the constant to the Y (endog) variable instead of the X (exog) variable.

The Answer

from __future__ import print_function
import patsy
import numpy as np
import pandas as pd
import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.regression.quantile_regression import QuantReg

data = sm.datasets.engel.load_pandas().data
data = sm.add_constant(data)

mod = QuantReg(data['foodexp'], data[['const', 'income']])
res = mod.fit(q=.5)
print(res.summary())

                         QuantReg Regression Results                          
==============================================================================
Dep. Variable:                foodexp   Pseudo R-squared:               0.6206
Model:                       QuantReg   Bandwidth:                       64.51
Method:                 Least Squares   Sparsity:                        209.3
Date:                Fri, 09 Oct 2015   No. Observations:                  235
Time:                        22:24:47   Df Residuals:                      233
                                        Df Model:                            1
==============================================================================
                 coef    std err          t      P>|t|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
const         81.4823     14.634      5.568      0.000        52.649   110.315
income         0.5602      0.013     42.516      0.000         0.534     0.586
==============================================================================

The condition number is large, 2.38e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

As an FYI, what I find interesting is that add_constant() just adds a column of 1s to your data. More information about add_constant() can be found here.

Launder

Constant can also be added like this: mod = QuantReg(data['foodexp'], sm.add_constant(data.income)) – Taishataisho