Python?OLS?雙向逐步回歸方式

更新時(shí)間：2024年05月16日 09:55:46 作者：AdamShyly

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Python OLS 雙向逐步回歸

算法基本思路

首先需要確定一個(gè)因變量y以此構(gòu)建一元回歸方程

再找到已通過(guò)顯著性檢驗(yàn)的一元線性回歸方程中F值最大的解釋變量x0

將其并入回歸方程中

再分別將剩余的解釋變量與解釋變量x0作為OLS函數(shù)的自變量集擬合回歸方程

同樣找出其中F值最大的自變量集

如果該自變量集均能通過(guò)顯著性檢驗(yàn)則將該解釋變量并入回歸方程中并進(jìn)行下一輪的迭代

否則舍棄該解釋變量

并找出F值第二大的自變量集繼續(xù)對(duì)其進(jìn)行顯著性檢驗(yàn)

import pandas as pd
import numpy as np
import statsmodels.api as sm
 
 
def test_significance(data, dv, src_idvs):
    model = sm.OLS(data.loc[:, dv], data.loc[:, src_idvs]).fit()
    for p in model.pvalues:
        if p > 0.05:
            return False
    else:
        return True
 
 
def find_max_F(data, dv, idvs, res_idvs):
    F_max = -1
    idv_F_max = None
    res_model = None
    for idv in idvs:
        new_idvs = res_idvs.copy()
        new_idvs.append(idv)  # 加入新解釋變量找出F最大值
        model = sm.OLS(data.loc[:, dv], sm.add_constant(
            data.loc[:, new_idvs])).fit()
        F = model.fvalue
        if F > F_max:
            F_max = F
            idv_F_max = idv
            res_model = model
    return F_max, idv_F_max, res_model
 
 
def stepwise_regression(data, dv, idvs=None):  # 向前向后逐步回歸
    res_idvs = []
    src_idvs = idvs.copy()
    res_models = []
    for step in range(len(idvs)):
        isExit = False
        while True:
            F, idv, model = find_max_F(
                data, dv, src_idvs, res_idvs)  # 求出F最大值以及對(duì)應(yīng)的解釋變量
 
            if model == None:  # 多元線性擬合失敗
                print("第{0}步擬合線性失敗".format(step + 1))
                isExit = True
                break
 
            res_idvs.append(idv)
 
            # 沒(méi)有新解釋變量并入回歸方程中
            if model.f_pvalue >= 0.05 or not test_significance(data, dv, res_idvs):
                res_idvs.pop()  # 移除該解釋變量
                src_idvs.remove(idv)
                print("第{0}步移除解釋變量{1}".format(step + 1, idv))
                if len(src_idvs) == 0:  # 該輪for循環(huán)并沒(méi)有解釋變量能夠并入回歸方程中
                    isExit = True
                    break
            else:  # 找到新解釋變量，結(jié)束While循環(huán)
                print("第{0}步并入解釋變量{1}".format(step + 1, idv))
                res_models.append(model)
                break
        if isExit:  # 提前結(jié)束逐步回歸
            break
        else:
            src_idvs = []
            for idv in idvs:
                if idv not in res_idvs:
                    src_idvs.append(idv)
    return res_idvs, res_models
 
 
data = pd.read_excel('./normalization.xlsx')
 
equations = []
stdouts = []
for column in data.columns:
    idvs = list(data.columns.copy())
    idvs.remove(column)
    res, models = stepwise_regression(data=data, dv=column, idvs=idvs)
    equation = 'y = '
    stdout = 'y為' + column + '、'
    for index in range(len(res)):
        equation += str(models[index].params[1]) + ' * x' + str(index)
        stdout += 'x' + str(index) + '為' +  res[index]
        if index != len(res) - 1:
            equation += ' + '
            stdout += '、'
    equations.append(equation)
    stdouts.append(stdout)
 
with open(file='./MultivariateLinearity.txt', mode='w', encoding='utf-8') as f:
    for index in range(len(equations)):
        f.write(equations[index] + '\n其中: ' + stdouts[index] + '\n')