zhr zhr - 1 month ago 8
Python Question

statistical summary table in sklearn.linear_model.ridge?

In OLS form StatsModels, results.summary shows the summary of regression results (such as AIC, BIC, R-squared, ...).

Is there any way to have this summary table in sklearn.linear_model.ridge?

I do appreciate if someone guide me. Thank you.

Answer

As I know, there is no R(or Statsmodels)-like summary table in sklearn. (Please check this answer)

Instead, if you need it, there is statsmodels.regression.linear_model.OLS.fit_regularized class. (L1_wt=0 for ridge regression.)

For now, it seems that model.fit_regularized(~).summary() returns None despite of docstring below. But the object has params, summary() can be used somehow.

Returns: A RegressionResults object, of the same type returned by fit.

Example.

Sample data is not for ridge regression, but I will try anyway.

In.

import numpy as np
import pandas as pd
import statsmodels
import statsmodels.api as sm
import matplotlib.pyplot as plt

statsmodels.__version__

Out.

'0.8.0rc1'

In.

data = sm.datasets.ccard.load()

print "endog: " + data.endog_name
print "exog: " + ', '.join(data.exog_name)

data.exog[:5, :]

Out.

endog: AVGEXP
exog: AGE, INCOME, INCOMESQ, OWNRENT
Out[2]:
array([[ 38.    ,   4.52  ,  20.4304,   1.    ],
       [ 33.    ,   2.42  ,   5.8564,   0.    ],
       [ 34.    ,   4.5   ,  20.25  ,   1.    ],
       [ 31.    ,   2.54  ,   6.4516,   0.    ],
       [ 32.    ,   9.79  ,  95.8441,   1.    ]])

In.

y, X = data.endog, data.exog

model = sm.OLS(y, X)
results_fu = model.fit()

print results_fu.summary()

Out.

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.543
Model:                            OLS   Adj. R-squared:                  0.516
Method:                 Least Squares   F-statistic:                     20.22
Date:                Wed, 19 Oct 2016   Prob (F-statistic):           5.24e-11
Time:                        17:22:48   Log-Likelihood:                -507.24
No. Observations:                  72   AIC:                             1022.
Df Residuals:                      68   BIC:                             1032.
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
x1            -6.8112      4.551     -1.497      0.139     -15.892       2.270
x2           175.8245     63.743      2.758      0.007      48.628     303.021
x3            -9.7235      6.030     -1.613      0.111     -21.756       2.309
x4            54.7496     80.044      0.684      0.496    -104.977     214.476
==============================================================================
Omnibus:                       76.325   Durbin-Watson:                   1.692
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              649.447
Skew:                           3.194   Prob(JB):                    9.42e-142
Kurtosis:                      16.255   Cond. No.                         87.5
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

In.

frames = []
for n in np.arange(0, 0.25, 0.05).tolist():
    results_fr = model.fit_regularized(L1_wt=0, alpha=n, start_params=results_fu.params)

    results_fr_fit = sm.regression.linear_model.OLSResults(model, 
                                                           results_fr.params, 
                                                           model.normalized_cov_params)
    frames.append(np.append(results_fr.params, results_fr_fit.ssr))

    df = pd.DataFrame(frames, columns=data.exog_name + ['ssr*'])
df.index=np.arange(0, 0.25, 0.05).tolist()
df.index.name = 'alpha*'
df.T

Out.

enter image description here

In.

%matplotlib inline

fig, ax = plt.subplots(1, 2, figsize=(14, 4))

ax[0] = df.iloc[:, :-1].plot(ax=ax[0])
ax[0].set_title('Coefficient')

ax[1] = df.iloc[:, -1].plot(ax=ax[1])
ax[1].set_title('SSR')

Out.

enter image description here

In.

results_fr = model.fit_regularized(L1_wt=0, alpha=0.04, start_params=results_fu.params)
final = sm.regression.linear_model.OLSResults(model, 
                                              results_fr.params, 
                                              model.normalized_cov_params)

print final.summary()

Out.

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.543
Model:                            OLS   Adj. R-squared:                  0.516
Method:                 Least Squares   F-statistic:                     20.17
Date:                Wed, 19 Oct 2016   Prob (F-statistic):           5.46e-11
Time:                        17:22:49   Log-Likelihood:                -507.28
No. Observations:                  72   AIC:                             1023.
Df Residuals:                      68   BIC:                             1032.
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
x1            -5.6375      4.554     -1.238      0.220     -14.724       3.449
x2           159.1412     63.781      2.495      0.015      31.867     286.415
x3            -8.1360      6.034     -1.348      0.182     -20.176       3.904
x4            44.2597     80.093      0.553      0.582    -115.564     204.083
==============================================================================
Omnibus:                       76.819   Durbin-Watson:                   1.694
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              658.948
Skew:                           3.220   Prob(JB):                    8.15e-144
Kurtosis:                      16.348   Cond. No.                         87.5
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.