python实现逐步回归

逐步回归（Stepwise Regression）是一种特征选择方法，可以用于多元线性回归模型中，它通过逐步加入或删除变量的方式来构建模型。Python实现逐步回归可以使用statsmodels库的OLS函数。

以下是一个简单的示例代码：

import pandas as pd
import statsmodels.api as sm

# 加载数据
data = pd.read_csv('data.csv')

# 定义自变量和因变量
X = data[['x1', 'x2', 'x3', 'x4']]
y = data['y']

# 逐步回归
def stepwise_selection(X, y, initial_list=[], threshold_in=0.01, threshold_out=0.05, verbose=True):
    included = list(initial_list)
    while True:
        changed = False
        excluded = list(set(X.columns) - set(included))
        new_pval = pd.Series(index=excluded)
        for new_column in excluded:
            model = sm.OLS(y, sm.add_constant(pd.DataFrame(X[included + [new_column]]))).fit()
            new_pval[new_column] = model.pvalues[new_column]
        min_pval = new_pval.min()
        if min_pval < threshold_in:
            best_feature = new_pval.argmin()
            included.append(best_feature)
            changed = True
            if verbose:
                print('Add  {:30} with p-value {:.6}'.format(best_feature, min_pval))
        model = sm.OLS(y, sm.add_constant(pd.DataFrame(X[included]))).fit()
        # 使用f-test检验是否需要移除特征
        pvalues = model.pvalues.iloc[1:]
        worst_pval = pvalues.max()
        if worst_pval > threshold_out:
            changed = True
            worst_feature = pvalues.argmax()
            included.remove(worst_feature)
            if verbose:
                print('Drop {:30} with p-value {:.6}'.format(worst_feature, worst_pval))
        if not changed:
            break
    return included

result = stepwise_selection(X, y)
print('resulting features:')
print(result)

上面的代码中，stepwise_selection函数实现了逐步回归的过程。函数的输入包括自变量X、因变量y、初始特征列表（默认为空）、加入特征的显著性水平和移除特征的显著性水平。函数的输出是逐步回归后选出的特征列表。