python - 如何在逻辑回归中使用权重

Question

我想在 Python 中计算(加权)逻辑回归。计算权重以调整样本关于总体的分布。但是，如果我使用权重，结果不会改变。

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

数据看起来像这样。目标变量是 VISIT .特征是除 WEIGHT_both 之外的所有其他变量(这是我想要使用的重量)。

df.head() 

WEIGHT_both VISIT   Q19_1   Q19_2   Q19_3   Q19_4   Q19_5   Q19_6   Q19_7   Q19_8   ... Q19_23  Q19_24  Q19_25  Q19_26  Q19_27  Q19_28  Q19_29  Q19_30  Q19_31  Q19_32
0   0.022320    1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 ... 4.0 4.0 1.0 1.0 1.0 1.0 2.0 3.0 3.0 2.0
1   0.027502    1.0 3.0 2.0 2.0 2.0 3.0 4.0 3.0 2.0 ... 3.0 2.0 2.0 2.0 2.0 4.0 2.0 4.0 2.0 2.0
2   0.022320    1.0 2.0 3.0 1.0 4.0 3.0 3.0 3.0 2.0 ... 3.0 3.0 3.0 2.0 2.0 1.0 2.0 2.0 1.0 1.0
3   0.084499    1.0 2.0 2.0 2.0 2.0 2.0 4.0 1.0 1.0 ... 2.0 2.0 1.0 1.0 1.0 2.0 1.0 2.0 1.0 1.0
4   0.022320    1.0 3.0 4.0 3.0 3.0 3.0 2.0 3.0 3.0 ... 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

没有权重，模型看起来像这样:

X = df.drop('WEIGHT_both', axis = 1)
X = X.drop('VISIT', axis = 1)
X = sm.add_constant(X)
w = = df['WEIGHT_both']
Y= df['VISIT']

fit = sm.Logit(Y, X).fit()

fit.summary()


Dep. Variable:  VISIT   No. Observations:   7971
Model:  Logit   Df Residuals:   7938
Method: MLE Df Model:   32
Date:   Sun, 05 Jul 2020    Pseudo R-squ.:  0.2485
Time:   16:41:12    Log-Likelihood: -3441.2
converged:  True    LL-Null:    -4578.8
Covariance Type:    nonrobust   LLR p-value:    0.000
coef    std err z   P>|z|   [0.025  0.975]
const   3.8098  0.131   29.126  0.000   3.553   4.066
Q19_1   -0.1116 0.063   -1.772  0.076   -0.235  0.012
Q19_2   -0.2718 0.061   -4.483  0.000   -0.391  -0.153
Q19_3   -0.2145 0.061   -3.519  0.000   -0.334  -0.095

使用样本权重，结果如下所示(无变化):

fit2 = sm.Logit(Y, X, sample_weight = w).fit() 
# same thing if I use class_weight

fit2.summary()


Dep. Variable:  VISIT   No. Observations:   7971
Model:  Logit   Df Residuals:   7938
Method: MLE Df Model:   32
Date:   Sun, 05 Jul 2020    Pseudo R-squ.:  0.2485
Time:   16:41:12    Log-Likelihood: -3441.2
converged:  True    LL-Null:    -4578.8
Covariance Type:    nonrobust   LLR p-value:    0.000
coef    std err z   P>|z|   [0.025  0.975]
const   3.8098  0.131   29.126  0.000   3.553   4.066
Q19_1   -0.1116 0.063   -1.772  0.076   -0.235  0.012
Q19_2   -0.2718 0.061   -4.483  0.000   -0.391  -0.153
Q19_3   -0.2145 0.061   -3.519  0.000   -0.334  -0.095

我用其他程序(例如 SPSS、R)计算了回归。加权结果必须不同。
这是一个示例(R 代码)。
没有权重(结果与 Python 代码相同):

fit = glm(VISIT~., data = df[ -c(1)] , family = "binomial")

summary(fit)

Call:
glm(formula = VISIT ~ ., family = "binomial", data = df[-c(1)])

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.1216  -0.6984   0.3722   0.6838   2.1083  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  3.80983    0.13080  29.126  < 2e-16 ***
Q19_1       -0.11158    0.06296  -1.772 0.076374 .  
Q19_2       -0.27176    0.06062  -4.483 7.36e-06 ***
Q19_3       -0.21451    0.06096  -3.519 0.000434 ***
Q19_4        0.22417    0.05163   4.342 1.41e-05 ***

带重量:

fit2 = glm(VISIT~., data = df[ -c(1)],  weights = df$WEIGHT_both, family = "binomial")


summary(fit2)

Call:
glm(formula = VISIT ~ ., family = "binomial", data = df[-c(1)], 
    weights = df$WEIGHT_both)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.4894  -0.3315   0.1619   0.2898   3.7878  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  4.950e-01  1.821e-01   2.718 0.006568 ** 
Q19_1       -6.497e-02  8.712e-02  -0.746 0.455835    
Q19_2       -1.720e-02  8.707e-02  -0.198 0.843362    
Q19_3       -1.114e-01  8.436e-02  -1.320 0.186743    
Q19_4        1.898e-02  7.095e-02   0.268 0.789066   

知道如何在逻辑回归中使用权重吗？

Answer 1

我认为一种方法是使用 smf.glm()您可以在其中提供权重 freq_weights , 你应该检查这个 section on weighted glm看看它是否是你想要实现的。下面我提供一个例子，它的使用方式与 weights= 相同。在 R 中:

import pandas as pd
import numpy as np
import seaborn as sns
import statsmodels.formula.api as smf
import statsmodels.api as sm

data = sns.load_dataset("iris") 
data['species'] = (data['species'] == "versicolor").astype(int)

fit = smf.glm("species ~ sepal_length + sepal_width + petal_length + petal_width",
              family=sm.families.Binomial(),data=data).fit()

fit.summary()

    coef         std err    z   P>|z|   [0.025  0.975]
Intercept        7.3785 2.499   2.952   0.003   2.480   12.277
sepal_length    -0.2454 0.650   -0.378  0.706   -1.518  1.028
sepal_width     -2.7966 0.784   -3.569  0.000   -4.332  -1.261
petal_length     1.3136 0.684   1.921   0.055   -0.027  2.654
petal_width     -2.7783 1.173   -2.368  0.018   -5.078  -0.479

现在提供权重:

wts = np.repeat(np.arange(1,6),30)
fit = smf.glm("species ~ sepal_length + sepal_width + petal_length + petal_width",
              family=sm.families.Binomial(),data=data,freq_weights=wts).fit()
fit.summary()

    coef         std err    z   P>|z|   [0.025  0.975]
Intercept        8.7146 1.444   6.036   0.000   5.885   11.544
sepal_length    -0.2053 0.359   -0.571  0.568   -0.910  0.499
sepal_width     -2.7293 0.454   -6.012  0.000   -3.619  -1.839
petal_length     0.8920 0.365   2.440   0.015   0.176   1.608
petal_width     -2.8420 0.622   -4.570  0.000   -4.061  -1.623

所以在 R 中你有未加权的:

glm(Species ~ .,data=data,family=binomial)

Call:  glm(formula = Species ~ ., family = binomial, data = data)

Coefficients:
 (Intercept)  Sepal.Length   Sepal.Width  Petal.Length   Petal.Width  
      7.3785       -0.2454       -2.7966        1.3136       -2.7783  

Degrees of Freedom: 149 Total (i.e. Null);  145 Residual
Null Deviance:      191 
Residual Deviance: 145.1    AIC: 155.1

和加权模型

glm(Species ~ .,data=data,family=binomial,weights=rep(1:5,each=30))

Call:  glm(formula = Species ~ ., family = binomial, data = data, weights = rep(1:5, 
    each = 30))

Coefficients:
 (Intercept)  Sepal.Length   Sepal.Width  Petal.Length   Petal.Width  
      8.7146       -0.2053       -2.7293        0.8920       -2.8420  

Degrees of Freedom: 149 Total (i.e. Null);  145 Residual
Null Deviance:      572.9 
Residual Deviance: 448.9    AIC: 458.9