逐步回归分析的代码以及示例

以下是Python中使用逐步回归分析进行变量筛选的示例代码：

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

# 读取数据
data = pd.read_csv('data.csv')
x = data.drop(columns=['target'])
y = data['target']

# 前向选择
def forward_select(data, target):
    variate = set(data.columns)
    selected = []
    current_score, best_new_score = float('inf'), float('inf')
    while variate and current_score == best_new_score:
        scores_with_candidates = []
        for candidate in variate:
            formula = "{} ~ {}".format(target, ' + '.join(selected + [candidate]))
            score = sm.OLS.from_formula(formula, data).fit().aic
            scores_with_candidates.append((score, candidate))
        scores_with_candidates.sort()
        best_new_score, best_candidate = scores_with_candidates.pop(0)
        if current_score > best_new_score:
            current_score = best_new_score
            selected.append(best_candidate)
            variate.remove(best_candidate)
    formula = "{} ~ {}".format(target, ' + '.join(selected))
    model = sm.OLS.from_formula(formula, data)
    result = model.fit()
    return result

# 后向消元
def backward_eliminate(data, target):
    variate = set(data.columns)
    selected = list(variate)
    current_score, best_new_score = float('inf'), float('inf')
    while variate and current_score == best_new_score:
        scores_with_candidates = []
        for candidate in variate:
            formula = "{} ~ {}".format(target, ' + '.join(selected.remove(candidate)))
            score = sm.OLS.from_formula(formula, data).fit().aic
            scores_with_candidates.append((score, candidate))
        scores_with_candidates.sort()
        best_new_score, best_candidate = scores_with_candidates.pop(0)
        if current_score > best_new_score:
            current_score = best_new_score
            selected.remove(best_candidate)
            variate.remove(best_candidate)
    formula = "{} ~ {}".format(target, ' + '.join(selected))
    model = sm.OLS.from_formula(formula, data)
    result = model.fit()
    return result

# 双向搜索
def stepwise_selection(data, target):
    variate = set(data.columns)
    selected = []
    current_score, best_new_score = float('inf'), float('inf')
    while variate and current_score == best_new_score:
        forward_scores_with_candidates = []
        for candidate in variate:
            formula = "{} ~ {}".format(target, ' + '.join(selected + [candidate]))
            score = sm.OLS.from_formula(formula, data).fit().aic
            forward_scores_with_candidates.append((score, candidate))
        forward_scores_with_candidates.sort()
        best_forward_new_score, best_forward_candidate = forward_scores_with_candidates.pop(0)
        
        backward_scores_with_candidates = []
        for candidate in selected:
            formula = "{} ~ {}".format(target, ' + '.join(selected.remove(candidate)))
            score = sm.OLS.from_formula(formula, data).fit().aic
            backward_scores_with_candidates.append((score, candidate))
        backward_scores_with_candidates.sort()
        best_backward_new_score, best_backward_candidate = backward_scores_with_candidates.pop(0)
        
        if best_forward_new_score < best_backward_new_score and current_score > best_forward_new_score:
            current_score = best_forward_new_score
            selected.append(best_forward_candidate)
            variate.remove(best_forward_candidate)
        elif current_score > best_backward_new_score:
            current_score = best_backward_new_score
            selected.remove(best_backward_candidate)
            variate.add(best_backward_candidate)
    formula = "{} ~ {}".format(target, ' + '.join(selected))
    model = sm.OLS.from_formula(formula, data)
    result = model.fit()
    return result

# 前向选择示例
forward_select_result = forward_select(data, 'target')
print(forward_select_result.summary())

# 后向消元示例
backward_eliminate_result = backward_eliminate(data, 'target')
print(backward_eliminate_result.summary())

# 双向搜索示例
stepwise_selection_result = stepwise_selection(data, 'target')
print(stepwise_selection_result.summary())

这里使用了statsmodels库进行线性回归分析，其中forward_select()、backward_eliminate()和stepwise_selection()分别实现了前向选择、后向消元和双向搜索。每个函数的输入为数据集和目标变量名称，输出为线性回归模型的结果。在示例中，分别用三种方法对数据集进行了变量筛选，并输出了各自的结果摘要。