Python实现自变量选择：所有子集回归、后退法与逐步回归详解

import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
from itertools import combinations
def allziji(df):
    
    list1 = [1,2,3]
    n = 18
    R2 = []
    names = []
    #找到所有子集，并依次循环
    for a in range(len(list1)+1):
        for b in combinations(list1,a+1):
            p = len(list(b))
 
            data1 = pd.concat([df.iloc[:,i-1] for i in list(b) ],axis = 1)#结合所需因子
            
            name = "y~"+("+".join(data1.columns))#组成公式
            
            data = pd.concat([df['y'],data1],axis=1)#结合自变量和因变量
            
            result = smf.ols(name,data=data).fit()#建模
            #计算R2a
            r2 = (n-1)/(n-p-1)
            r2 = r2 * (1-result.rsquared**2)
            r2 = 1 - r2
            R2.append(r2)
            names.append(name)
    finall = {"公式":names,              "R2a":R2}
    data = pd.DataFrame(finall)
    print("""根据自由度调整复决定系数准则得到：
        最优子集回归模型为：{}；
        其R2a值为：{}""".format(data.iloc[data['R2a'].argmax(),0],data.iloc[data['R2a'].argmax(),1]))
    result = smf.ols(name,data=df).fit()#建模
    print()
    print(result.summary())

df = pd.read_csv("data5.csv")
allziji(df)

import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
 
def backward(df):
    all_bianliang = [i for i in range(0,9)]#备退因子
    ceshi = [i for i in range(0,9)]#存放加入单个因子后的模型
    zhengshi = [i for i in range(0,9)]#收集确定因子
    data1 = pd.concat([df.iloc[:,i+1] for i in ceshi ],axis = 1)#结合所需因子
    name = 'y~'+'+'.join(data1.columns)
    result = smf.ols(name,data=df).fit()#建模
    c0 = result.aic #最小aic
    delete = []#已删元素
    while(all_bianliang):
        aic = []#存放aic
 
        for i in all_bianliang:
            ceshi = [i for i in zhengshi]
            ceshi.remove(i)
            data1 = pd.concat([df.iloc[:,i+1] for i in ceshi ],axis = 1)#结合所需因子
            name = "y~"+("+".join(data1.columns))#组成公式
            data = pd.concat([df['y'],data1],axis=1)#结合自变量和因变量
            result = smf.ols(name,data=data).fit()#建模
            aic.append(result.aic)#将所有aic存入
 
        if min(aic)>c0:#aic已经达到最小
            data1 = pd.concat([df.iloc[:,i+1] for i in zhengshi ],axis = 1)#结合所需因子
            name = "y~"+("+".join(data1.columns))#组成公式
            break
        else:
            zhengshi.remove(all_bianliang[aic.index(min(aic))])#查找最小的aic并将最小的因子存入正式的模型列表当中
 
        c0 = min(aic)
        delete.append(aic.index(min(aic)))
        all_bianliang.remove(all_bianliang[delete[-1]])#删除已删因子
 
    name = "y~"+("+".join(data1.columns))#组成公式
    print("最优模型为：{}，其aic为：{}".format(name,c0))
    result = smf.ols(name,data=df).fit()#建模
    print()
    print(result.summary())

df = pd.read_csv("data3.1.csv",encoding='gbk')
backward(df)

import pandas as pd
import numpy as np
import statsmodels.api as sm
import statsmodels.formula.api as smf
def zhubuhuigui(df):
    forward = [i for i in range(0,4)]#备选因子
    backward = []#备退因子
    ceshi = []#存放加入单个因子后的模型
    zhengshi = []#收集确定因子
    delete = []#被删因子

    while forward:
        forward_aic = []#前进aic
        backward_aic = []#后退aic

        for i in forward:
            ceshi = [j for j in zhengshi]
            ceshi.append(i)
            data1 = pd.concat([df.iloc[:,i] for i in ceshi ],axis = 1)#结合所需因子
            name = "y~"+("+".join(data1.columns))#组成公式
            data = pd.concat([df['y'],data1],axis=1)#结合自变量和因变量
            result = smf.ols(name,data=data).fit()#建模
            forward_aic.append(result.aic)#将所有aic存入

        for i in backward:
            if (len(backward)==1):
                pass

            else:
                ceshi = [j for j in zhengshi]
                ceshi.remove(i)
                data1 = pd.concat([df.iloc[:,i] for i in ceshi ],axis = 1)#结合所需因子
                name = "y~"+("+".join(data1.columns))#组成公式
                data = pd.concat([df['y'],data1],axis=1)#结合自变量和因变量
                result = smf.ols(name,data=data).fit()#建模
                backward_aic.append(result.aic)#将所有aic存入

        if backward_aic:
            if forward_aic:
                c0 = min(min(backward_aic),min(forward_aic))

            else:
                c0 = min(backward_aic)

        else:
            c0 = min(forward_aic)

        if c0 in backward_aic:
            zhengshi.remove(backward[backward_aic.index(c0)])
            delete.append(backward_aic.index(c0))
            backward.remove(backward[delete[-1]])#删除已删因子
            forward.append(backward[delete[-1]])
        else:
            zhengshi.append(forward[forward_aic.index(c0)])#查找最小的aic并将最小的因子存入正式的模型列表当中
            forward.remove(zhengshi[-1])#删除已有因子
            backward.append(zhengshi[-1])
 
    name = "y~"+("+".join(data1.columns))#组成公式
    print("最优模型为：{}，其aic为：{}".format(name,c0))
    result = smf.ols(name,data=data).fit()#建模
    print()
    print(result.summary())

df = pd.read_csv("data5.5.csv",encoding='gbk')
zhubuhuigui(df)