在statsmodels中如何获取无截距的全对比效应结果？

考虑以下简单示例：

import pandas as pd
from statsmodels.formula.api import ols

url = "https://stats.idre.ucla.edu/stat/data/hsb2.csv"
hsb2 = pd.read_table(url, delimiter=",")
hsb2.head()
# 输出示例：
#     id  female  race  ses  schtyp  prog  read  write  math  science  socst
# 0   70       0     4    1       1     1    57     52    41       47     57
# 1  121       1     4    2       1     3    68     59    53       63     61

我有两个感兴趣的分类变量（race和female），希望计算这两个变量所有可能组合对应的read分数均值的t统计量。目前可以通过statsmodels中的C()符号，将write对这两个分类变量的全交互项进行回归，间接获取该信息：

mod = ols("write ~ C(race)*C(female)", data=hsb2)
res = mod.fit()
print(res.summary())

回归输出如下：

OLS Regression Results                            
==============================================================================
Dep. Variable:                  write   R-squared:                       0.171
Model:                            OLS   Adj. R-squared:                  0.140
Method:                 Least Squares   F-statistic:                     5.642
Date:                Fri, 25 Aug 2023   Prob (F-statistic):           6.16e-06
Time:                        11:02:32   Log-Likelihood:                -714.39
No. Observations:                 200   AIC:                             1445.
Df Residuals:                     192   BIC:                             1471.
Df Model:                           7                                         
Covariance Type:            nonrobust                                         
===============================================================================================
                                  coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------------
Intercept                      44.3846      2.437     18.210      0.000      39.577      49.192
C(race)[T.2]                   11.2821      5.629      2.004      0.046       0.180      22.385
C(race)[T.3]                    2.6154      4.120      0.635      0.526      -5.511      10.742
C(race)[T.4]                    6.9095      2.660      2.597      0.010       1.663      12.156
C(female)[T.1]                  4.5245      3.600      1.257      0.210      -2.577      11.626
C(race)[T.2]:C(female)[T.1]    -1.3161      6.954     -0.189      0.850     -15.032      12.400
C(race)[T.3]:C(female)[T.1]    -2.6783      5.471     -0.490      0.625     -13.470       8.113
C(race)[T.4]:C(female)[T.1]     0.6749      3.886      0.174      0.862      -6.990       8.340
==============================================================================
Omnibus:                        6.095   Durbin-Watson:                   1.906
Prob(Omnibus):                  0.047   Jarque-Bera (JB):                5.710
Skew:                          -0.356   Prob(JB):                       0.0576
Kurtosis:                       2.578   Cond. No.                         23.2
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

但我希望在回归输出中查看全对比效应（无截距项），即无需手动累加主效应和交互项，直接得到female和race每个组合的平均得分。能否在statsmodels中实现这一需求？

完全可以实现，以下两种方式可直接获取分类变量组合的均值及对应的t统计量：

方法1：无截距项的全交叉项模型 #

在公式中添加0 +或-1去掉截距，同时用C(race):C(female)表示两个变量的全交叉组合（等价于C(race)*C(female) - C(race) - C(female)），回归系数将直接对应每个组合的均值：

mod = ols("write ~ 0 + C(race):C(female)", data=hsb2)
res = mod.fit()
print(res.summary())

输出的每个系数就是race和female对应组合的write分数均值，同时附带标准误、t值和p值。

方法2：生成组合变量后回归 #

先将两个分类变量合并为一个新的组合变量，再用无截距模型回归，变量名会更直观：

# 生成组合变量
hsb2['race_female'] = hsb2.apply(lambda x: f"race_{x['race']}_female_{x['female']}", axis=1)
# 无截距回归
mod = ols("write ~ 0 + C(race_female)", data=hsb2)
res = mod.fit()
print(res.summary())

结果验证 #

可以通过分组均值验证回归系数的准确性：

print(hsb2.groupby(['race', 'female'])['write'].mean())

输出的分组均值会和回归系数完全一致。

内容的提问来源于stack exchange，提问作者ℕʘʘḆḽḘ