如何在Python中向GLM添加零和约束？

我在Python中使用statsmodel

glm

函数设置了一个模型，但现在我想向模型添加一个零和约束

该模型定义如下：

import statsmodels.formula.api as smf
model = smf.glm(formula="A ~ B + C + D", data=data, family=sm.families.Poisson()).fit()

在R中，要添加约束，我只需执行以下操作：

model <- glm(A ~ B + C + D –1, family=poisson(), data=data, contrasts=list(C="contr.sum", D="contr.sum"))

---

model这里有一个例子来说明
fit\u constrained
，使用高斯族，因为我没有很快找到一个带有分类变量的泊松例子

import pandas
import statsmodels.api as sm
from statsmodels.formula.api import glm

url = 'http://www.ats.ucla.edu/stat/data/hsb2.csv'
hsb2 = pandas.read_table(url, delimiter=",")

mod = glm("write ~ C(race) - 1", data=hsb2)
res = mod.fit()
print(res.summary())

所有系数相加为零的约束

res_c = mod.fit_constrained('C(race)[1] + C(race)[2] + C(race)[3] + C(race)[4] = 0')
print(res_c.summary())

                 Generalized Linear Model Regression Results                  
==============================================================================
Dep. Variable:                  write   No. Observations:                  200
Model:                            GLM   Df Residuals:                      197
Model Family:                Gaussian   Df Model:                            2
Link Function:               identity   Scale:                   1232.08314649
Method:                          IRLS   Log-Likelihood:                -993.41
Date:                Wed, 25 Mar 2015   Deviance:                   2.4149e+05
Time:                        16:42:37   Pearson chi2:                 2.41e+05
No. Iterations:                     1                                         
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
C(race)[1]     1.0002    221.565      0.005      0.996      -433.260   435.260
C(race)[2]   -41.1814    267.253     -0.154      0.878      -564.988   482.626
C(race)[3]    -6.3498    235.771     -0.027      0.979      -468.453   455.754
C(race)[4]    46.5311    100.184      0.464      0.642      -149.827   242.889
==============================================================================

Model has been estimated subject to linear equality constraints.

约束以逗号分隔，默认为等于零：

res_c2 = mod.fit_constrained('C(race)[1] + C(race)[2], C(race)[3] + C(race)[4]')
print(res_c2.summary())

最后的指纹

                 Generalized Linear Model Regression Results                  
==============================================================================
Dep. Variable:                  write   No. Observations:                  200
Model:                            GLM   Df Residuals:                      198
Model Family:                Gaussian   Df Model:                            1
Link Function:               identity   Scale:                   1438.99574167
Method:                          IRLS   Log-Likelihood:                -1008.9
Date:                Wed, 25 Mar 2015   Deviance:                   2.8204e+05
Time:                        16:42:37   Pearson chi2:                 2.82e+05
No. Iterations:                     1                                         
==============================================================================
                 coef    std err          z      P>|z|      [95.0% Conf. Int.]
------------------------------------------------------------------------------
C(race)[1]    13.6286    242.003      0.056      0.955      -460.689   487.946
C(race)[2]   -13.6286    242.003     -0.056      0.955      -487.946   460.689
C(race)[3]   -41.6606    111.458     -0.374      0.709      -260.115   176.794
C(race)[4]    41.6606    111.458      0.374      0.709      -176.794   260.115
==============================================================================

Model has been estimated subject to linear equality constraints.

我不确定patsy公式是如何工作的，因此如果存在多个分类解释变量，则不会降低任何级别。
这是否会将C和D的和分别强制为零？和对比度编码是否适用于此<代码>拟合约束

将用于此，并将转换设计矩阵。我需要检查，但我认为您需要的是一个包含两行的限制矩阵，在相应的列中有

1

，一行用于

C

级别，另一行用于

D

级别。嗯。。。您发布的内容似乎可以正常工作，但我遇到了一个错误，它甚至阻止了模型的创建。如果模型是“write~race-1”，我会得到

AttributeError:'GLM'对象没有属性“fit\u constrated”

，我会尝试使用“race=1”表示fit\u constrated。我得到了一个错误：数组不能为空John，在这种情况下没有什么可估计的。statsmodels中的模型不是针对这种情况设计的。在特定情况下，通常空数组行为将主要从numpy继承，这可能会得到支持。