scikit learn: how to check coefficients significance

Question

i tried to do a LR with SKLearn for a rather large dataset with ~600 dummy and only few interval variables (and 300 K lines in my dataset) and the resulting confusion matrix

Answer 1

Scikit-learn deliberately does not support statistical inference. If you want out-of-the-box coefficients significance tests (and much more), you can use Logit estimator from Statsmodels. This package mimics interface glm models in R, so you could find it familiar.

If you still want to stick to scikit-learn LogisticRegression, you can use asymtotic approximation to distribution of maximum likelihiood estimates. Precisely, for a vector of maximum likelihood estimates theta, its variance-covariance matrix can be estimated as inverse(H), where H is the Hessian matrix of log-likelihood at theta. This is exactly what the function below does:

import numpy as np
from scipy.stats import norm
from sklearn.linear_model import LogisticRegression

def logit_pvalue(model, x):
    """ Calculate z-scores for scikit-learn LogisticRegression.
    parameters:
        model: fitted sklearn.linear_model.LogisticRegression with intercept and large C
        x:     matrix on which the model was fit
    This function uses asymtptics for maximum likelihood estimates.
    """
    p = model.predict_proba(x)
    n = len(p)
    m = len(model.coef_[0]) + 1
    coefs = np.concatenate([model.intercept_, model.coef_[0]])
    x_full = np.matrix(np.insert(np.array(x), 0, 1, axis = 1))
    ans = np.zeros((m, m))
    for i in range(n):
        ans = ans + np.dot(np.transpose(x_full[i, :]), x_full[i, :]) * p[i,1] * p[i, 0]
    vcov = np.linalg.inv(np.matrix(ans))
    se = np.sqrt(np.diag(vcov))
    t =  coefs/se  
    p = (1 - norm.cdf(abs(t))) * 2
    return p

# test p-values
x = np.arange(10)[:, np.newaxis]
y = np.array([0,0,0,1,0,0,1,1,1,1])
model = LogisticRegression(C=1e30).fit(x, y)
print(logit_pvalue(model, x))

# compare with statsmodels
import statsmodels.api as sm
sm_model = sm.Logit(y, sm.add_constant(x)).fit(disp=0)
print(sm_model.pvalues)
sm_model.summary()

The outputs of print() are identical, and they happen to be coefficient p-values.

[ 0.11413093  0.08779978]
[ 0.11413093  0.08779979]

sm_model.summary() also prints a nicely formatted HTML summary.