---

name: statsmodels description: "Statsmodels 是 Python 首屈一指的统计建模库，提供涵盖多种统计方法的估计、推断和诊断工具。" license: BSD-3-Clause license metadata: skill-author: K-Dense Inc. risk: unknown source: community

Statsmodels：统计建模与计量经济学

概述

Statsmodels 是 Python 首屈一指的统计建模库，提供涵盖多种统计方法的估计、推断和诊断工具。当需要进行严谨的统计分析时（从简单线性回归到复杂时间序列模型和计量经济学分析），请使用此技能。

何时使用此技能

此技能适用于以下场景：

• 拟合回归模型（OLS、WLS、GLS、分位数回归）
• 执行广义线性建模（逻辑回归、泊松回归、Gamma 回归等）
• 分析离散结果（二元、多项、计数、有序）
• 进行时间序列分析（ARIMA、SARIMAX、VAR、预测）
• 运行统计检验和诊断
• 检验模型假设（异方差性、自相关、正态性）
• 检测异常值和强影响观测
• 比较模型（AIC/BIC、似然比检验）
• 估计因果效应
• 生成可发表的统计表格和推断结果

快速入门指南

线性回归（OLS）

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

# Prepare data - ALWAYS add constant for intercept
X = sm.add_constant(X_data)

# Fit OLS model
model = sm.OLS(y, X)
results = model.fit()

# View comprehensive results
print(results.summary())

# Key results
print(f"R-squared: {results.rsquared:.4f}")
print(f"Coefficients:\n{results.params}")
print(f"P-values:\n{results.pvalues}")

# Predictions with confidence intervals
predictions = results.get_prediction(X_new)
pred_summary = predictions.summary_frame()
print(pred_summary)  # includes mean, CI, prediction intervals

# Diagnostics
from statsmodels.stats.diagnostic import het_breuschpagan
bp_test = het_breuschpagan(results.resid, X)
print(f"Breusch-Pagan p-value: {bp_test[1]:.4f}")

# Visualize residuals
import matplotlib.pyplot as plt
plt.scatter(results.fittedvalues, results.resid)
plt.axhline(y=0, color='r', linestyle='--')
plt.xlabel('Fitted values')
plt.ylabel('Residuals')
plt.show()

逻辑回归（二元结果）

from statsmodels.discrete.discrete_model import Logit

# Add constant
X = sm.add_constant(X_data)

# Fit logit model
model = Logit(y_binary, X)
results = model.fit()

print(results.summary())

# Odds ratios
odds_ratios = np.exp(results.params)
print("Odds ratios:\n", odds_ratios)

# Predicted probabilities
probs = results.predict(X)

# Binary predictions (0.5 threshold)
predictions = (probs > 0.5).astype(int)

# Model evaluation
from sklearn.metrics import classification_report, roc_auc_score

print(classification_report(y_binary, predictions))
print(f"AUC: {roc_auc_score(y_binary, probs):.4f}")

# Marginal effects
marginal = results.get_margeff()
print(marginal.summary())

时间序列（ARIMA）

from statsmodels.tsa.arima.model import ARIMA
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

# Check stationarity
from statsmodels.tsa.stattools import adfuller

adf_result = adfuller(y_series)
print(f"ADF p-value: {adf_result[1]:.4f}")

if adf_result[1] > 0.05:
    # Series is non-stationary, difference it
    y_diff = y_series.diff().dropna()

# Plot ACF/PACF to identify p, q
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8))
plot_acf(y_diff, lags=40, ax=ax1)
plot_pacf(y_diff, lags=40, ax=ax2)
plt.show()

# Fit ARIMA(p,d,q)
model = ARIMA(y_series, order=(1, 1, 1))
results = model.fit()

print(results.summary())

# Forecast
forecast = results.forecast(steps=10)
forecast_obj = results.get_forecast(steps=10)
forecast_df = forecast_obj.summary_frame()

print(forecast_df)  # includes mean and confidence intervals

# Residual diagnostics
results.plot_diagnostics(figsize=(12, 8))
plt.show()

广义线性模型（GLM）

import statsmodels.api as sm

# Poisson regression for count data
X = sm.add_constant(X_data)
model = sm.GLM(y_counts, X, family=sm.families.Poisson())
results = model.fit()

print(results.summary())

# Rate ratios (for Poisson with log link)
rate_ratios = np.exp(results.params)
print("Rate ratios:\n", rate_ratios)

# Check overdispersion
overdispersion = results.pearson_chi2 / results.df_resid
print(f"Overdispersion: {overdispersion:.2f}")

if overdispersion > 1.5:
    # Use Negative Binomial instead
    from statsmodels.discrete.count_model import NegativeBinomial
    nb_model = NegativeBinomial(y_counts, X)
    nb_results = nb_model.fit()
    print(nb_results.summary())

核心统计建模能力

1. 线性回归模型

针对连续结果变量的全面线性模型套件，支持各种误差结构。