title: Logit estimator in `statsmodels` and `sklearn`
body: <p>I'm pretty sure it's a feature, not a bug, but I would like to know if there is a way to make <code>sklearn</code> and <code>statsmodels</code> match in their logit estimates. A very simple example:</p>
  
  <pre><code>import numpy as np
  import statsmodels.formula.api as sm
  from sklearn.linear_model import LogisticRegression
  
  np.random.seed(123)
  
  n = 100
  y = np.random.random_integers(0, 1, n)
  x = np.random.random((n, 2))
  # Constant term
  x[:, 0] = 1.
  </code></pre>
  
  <p>The estimates with <code>statsmodels</code>:</p>
  
  <pre><code>sm_lgt = sm.Logit(y, x).fit()
      Optimization terminated successfully.
               Current function value: 0.675320
               Iterations 4
  print sm_lgt.params
      [ 0.38442   -1.1429183]
  </code></pre>
  
  <p>And the estimates with <code>sklearn</code>:</p>
  
  <pre><code>sk_lgt = LogisticRegression(fit_intercept=False).fit(x, y)
  print sk_lgt.coef_
      [[ 0.16546794 -0.72637982]]
  </code></pre>
  
  <p>I think it's got to do with the implementation in <code>sklearn</code>, which uses some sort of regularization. Is there an option to estimate a barebones logit as in <code>statsmodels</code> (it's substantially faster and scales much more nicely). Also, does <code>sklearn</code> provide inference (standard errors) or marginal effects?</p>