如何在Python中执行Wald检验？特定假设检验的代码疑问

Great question! You're already on the right track using statsmodels' OLS implementation—here's how to run those Wald tests correctly with the wald_test() method built into the fitted results object:

Full Working Code #

from statsmodels.datasets import longley
import statsmodels.formula.api as smf

# Load the sample data
data = longley.load_pandas().data

# Define your hypotheses (including your target: Intercept=0, GNP=1)
hypothesis_0 = '(Intercept = 0, GNP = 0)'
hypothesis_1 = '(GNP = 0)'
hypothesis_2 = '(GNP = 1)'
hypothesis_3 = '(Intercept = 0, GNP = 1)'  # Your key hypothesis

# Fit the OLS regression model
results = smf.ols('TOTEMP ~ GNP', data).fit()

# Execute each Wald test
wald_0 = results.wald_test(hypothesis_0)
wald_1 = results.wald_test(hypothesis_1)
wald_2 = results.wald_test(hypothesis_2)
wald_3 = results.wald_test(hypothesis_3)  # This is the test you need

# Print the result for your target hypothesis
print("Wald Test Results: Intercept = 0 and GNP coefficient = 1")
print(wald_3)

How It Works #

• The wald_test() method accepts a string defining your null hypothesis using the exact variable names from your model (here, Intercept and GNP). For multiple constraints, separate them with commas inside the parentheses.
• The output will include:
  • A chi-squared test statistic
  • Degrees of freedom (equal to the number of constraints in your hypothesis—2 for hypothesis_3)
  • A p-value

Interpreting the Result #

• If the p-value is greater than your chosen significance level (e.g., 0.05), you fail to reject the null hypothesis that Intercept=0 and GNP=1.
• If the p-value is less than your significance level, you reject the null hypothesis.

Bonus: Custom Contrast Matrix (Optional) #

For more complex hypotheses, you can pass a contrast matrix instead of a string. For your target hypothesis, the matrix would look like this:

import numpy as np
contrast_matrix = np.array([[1, 0],  # Intercept = 0
                            [0, 1]]) # GNP = 1
wald_3_matrix = results.wald_test(contrast_matrix, value=[0, 1])
print(wald_3_matrix)

This gives the exact same result as the string method, but is useful for non-linear or more complex constraints.

内容的提问来源于stack exchange，提问作者파워뿡뿡이