模型系数的标准误差是协方差矩阵的对角线项的平方根。考虑以下：

• 设计矩阵：

$\textbf{X = }\begin{bmatrix} 1 & x_{1,1} & \ldots & x_{1,p} \\ 1 & x_{2,1} & \ldots & x_{2,p} \\ \vdots & \vdots & \ddots & \vdots \\ 1 & x_{n,1} & \ldots & x_{n,p} \end{bmatrix}$ ， 在哪里$x_{i,j}$是的价值$j$的预测器$i$观察。

（注意：这假定模型具有截距。）

• $\textbf{V = } \begin{bmatrix} \hat{\pi}_{1}(1 - \hat{\pi}_{1}) & 0 & \ldots & 0 \\ 0 & \hat{\pi}_{2}(1 - \hat{\pi}_{2}) & \ldots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \ldots & \hat{\pi}_{n}(1 - \hat{\pi}_{n}) \end{bmatrix}$ ， 在哪里$\hat{\pi}_{i}$表示用于观察的类成员的预测概率$i$.

协方差矩阵可以写成：

$\textbf{(X}^{T}\textbf{V}\textbf{X)}^{-1}$

这可以使用以下代码来实现：

import numpy as np
from sklearn import linear_model

# Initiate logistic regression object
logit = linear_model.LogisticRegression()

# Fit model. Let X_train = matrix of predictors, y_train = matrix of variable.
# NOTE: Do not include a column for the intercept when fitting the model.
resLogit = logit.fit(X_train, y_train)

# Calculate matrix of predicted class probabilities.
# Check resLogit.classes_ to make sure that sklearn ordered your classes as expected
predProbs = resLogit.predict_proba(X_train)

# Design matrix -- add column of 1's at the beginning of your X_train matrix
X_design = np.hstack([np.ones((X_train.shape[0], 1)), X_train])

# Initiate matrix of 0's, fill diagonal with each predicted observation's variance
V = np.diagflat(np.product(predProbs, axis=1))

# Covariance matrix
# Note that the @-operater does matrix multiplication in Python 3.5+, so if you're running
# Python 3.5+, you can replace the covLogit-line below with the more readable:
# covLogit = np.linalg.inv(X_design.T @ V @ X_design)
covLogit = np.linalg.inv(np.dot(np.dot(X_design.T, V), X_design))
print("Covariance matrix: ", covLogit)

# Standard errors
print("Standard errors: ", np.sqrt(np.diag(covLogit)))

# Wald statistic (coefficient / s.e.) ^ 2
logitParams = np.insert(resLogit.coef_, 0, resLogit.intercept_)
print("Wald statistics: ", (logitParams / np.sqrt(np.diag(covLogit))) ** 2)

话虽如此，statsmodels如果您想访问大量“开箱即用”的诊断程序，可能会是一个更好的包。

您的软件是否为您提供参数协方差（或方差-协方差）矩阵？如果是这样，则标准误差是该矩阵对角线的平方根。您可能想查阅教科书（或 google 获取大学讲义）以了解如何获取$V_\beta$线性和广义线性模型的矩阵。

如果您对推理感兴趣，那么您可能想看看statsmodels。标准误差和常见的统计测试可用。这是一个逻辑回归示例。