python-2.7 - Python中的logit回归和奇异矩阵错误

Question

我正在尝试对德国信用数据运行 logit 回归 (www4.stat.ncsu.edu/~boos/var.select/german.credit.html)。为了测试代码，我只使用了数值变量，并尝试使用以下代码对其结果进行回归。

import pandas as pd
import statsmodels.api as sm
import pylab as pl
import numpy as np

df = pd.read_csv("germandata.txt",delimiter=' ')
df.columns = ["chk_acc","duration","history","purpose","amount","savings_acc","employ_since","install_rate","pers_status","debtors","residence_since","property","age","other_plans","housing","existing_credit","job","no_people_liab","telephone","foreign_worker","admit"]

#pls note that I am only retaining numeric variables
cols_to_keep = ['admit','duration', 'amount', 'install_rate','residence_since','age','existing_credit','no_people_liab']

# rank of cols_to_keep is 8
print np.linalg.matrix_rank(df[cols_to_keep].values)
data = df[cols_to_keep]

data['intercept'] = 1.0

train_cols = data.columns[1:]

#to check the rank of train_cols, which in this case is 8
print np.linalg.matrix_rank(data[train_cols].values)

#fit logit model
logit = sm.Logit(data['admit'], data[train_cols])
result = logit.fit()

当我检查数据时，所有 8.0 列似乎都是独立的。尽管如此，我还是收到了奇异矩阵错误。你能帮忙吗？

谢谢

Answer 1

endog y 变量需要为零、一。在这个数据集中，它有 1 和 2 的值。如果我们减去 1，那么它就会产生结果。

>>> logit = sm.Logit(data['admit'] - 1, data[train_cols])
>>> result = logit.fit()
>>> print result.summary()
                           Logit Regression Results                           
==============================================================================
Dep. Variable:                  admit   No. Observations:                  999
Model:                          Logit   Df Residuals:                      991
Method:                           MLE   Df Model:                            7
Date:                Fri, 19 Sep 2014   Pseudo R-squ.:                 0.05146
Time:                        10:06:06   Log-Likelihood:                -579.09
converged:                       True   LL-Null:                       -610.51
                                        LLR p-value:                 4.103e-11
===================================================================================
                      coef    std err          z      P>|z|      [95.0% Conf. Int.]
-----------------------------------------------------------------------------------
duration            0.0261      0.008      3.392      0.001         0.011     0.041
amount           7.062e-05    3.4e-05      2.075      0.038      3.92e-06     0.000
install_rate        0.2039      0.073      2.812      0.005         0.062     0.346
residence_since     0.0411      0.067      0.614      0.539        -0.090     0.172
age                -0.0213      0.007     -2.997      0.003        -0.035    -0.007
existing_credit    -0.1560      0.130     -1.196      0.232        -0.412     0.100
no_people_liab      0.1264      0.201      0.628      0.530        -0.268     0.521
intercept          -1.5746      0.430     -3.661      0.000        -2.418    -0.732
===================================================================================

然而，在其他情况下，当我们评估它远离最佳时，例如在糟糕的起始值时，Hessian 可能不是正定的。在这些情况下，切换到不使用 Hessian 的优化器通常会成功。例如，scipy 的 'bfgs' 是一个很好的优化器，适用于许多情况

result = logit.fit(method='bfgs')