如何使用 statsmodels 中模型的常用包装器来应用交叉验证？

我在这里阅读了相关讨论：使用 statsmodel 估计和 scikit-learn 交叉验证，可能吗？ https://stackoverflow.com/questions/41045752/using-statsmodel-estimations-with-scikit-learn-cross-validation-is-it-possible

在链接的讨论中，建议使用以下模型的包装器statsmodels使得cross_val_score函数从sklearn可以使用库。该代码确实运行，但我不确定要提供什么参数。

示例代码：

class SMWrapper(BaseEstimator, RegressorMixin):
""" A sklearn-style wrapper for formula-based statsmodels regressors """
def __init__(self, model_class, formula, family, data):
    self.model_class = model_class      # choose the model from statsmodels.formula.api library (i.e. logit or glm)
    self.formula = formula              # expression using patsy syntax as required by statsmodels
    self.data = data                    # the full dataframe as required by statsmodels
    self.family = family                # the family argument as required by statsmodels

def fit(self, X=None, y=None):
    self.model = self.model_class(self.formula, data=self.data, family=self.family)
    self.results = self.model.fit()

def predict(self, X):
    return self.results.predict(X)

formula = 'wage ~ workhours + np.power(workhours, 3) + C(gender)'
wrappedModel = SMWrapper(model_class=glm, formula=formula, data=df, family=sm.families.Poisson(sm.families.links.log()))
-1*cross_val_score(wrappedModel, X=df[["workhours", "gender"]], y=df["wage"], scoring="neg_mean_squared_error", cv=10, error_score='raise')

问题：

• 我指定的是否正确X=df[["workhours", "gender"]] and y=df["wage"]作为参数cross_val_score? statsmodels只需要整个数据框df作为输入，公式由 patsy 语法指定。相比之下，sklearn模型需要单独的 X 和 y 参数。
• Does sklearn's cross_val_score也使用变量np.power(workhours, 3)在例子中？我认为确实如此，因为如果我重新排序公式，使得np.power(workhours, 3)是 ~ 之后的第一个变量，并省略工作时间，这样X=df["gender"]代替X=df[["workhours", "gender"]]，错误指出变量np.power(workhours, 3)未知。
• 如果我将公式改为wage ~ workhours + np.power(workhours, 3) + C(gender, Treatment(reference='female')). In statsmodels，这排除了女性，因此参考组是female。会不会sklearn型号相应改变？
• 为什么我需要参数X=None and y=None?

完整代码示例：

import pandas as pd
import numpy as np
import statsmodels.api as sm
from statsmodels.formula.api import glm
import random
from sklearn.model_selection import cross_val_score
from sklearn.base import BaseEstimator, RegressorMixin

# generate explanatory variables
x1 = np.random.normal(40, 4, 1000)
x2 = random.choices(["Male", "Female"], k=1000)
error = np.random.normal(0, 1, 1000)
y = 1234 + (4*x1) + error

# collect data in a dataframe
df = pd.DataFrame(zip(y, x1, x2), columns=['wage', 'workhours', 'gender'])

class SMWrapper(BaseEstimator, RegressorMixin):
    """ A sklearn-style wrapper for formula-based statsmodels regressors """
    def __init__(self, model_class, formula, family, data):
        self.model_class = model_class
        self.formula = formula
        self.data = data
        self.family = family
    def fit(self, X=None, y=None):
        self.model = self.model_class(self.formula, data=self.data, family=self.family)
        self.results = self.model.fit()
    def predict(self, X):
        return self.results.predict(X)

formula = 'wage ~ workhours + np.power(workhours, 3) + C(gender)'
wrappedModel = SMWrapper(model_class=glm, formula=formula, data=df, family=sm.families.Poisson(sm.families.links.log()))
-1*cross_val_score(wrappedModel, X=df[["workhours", "gender"]], y=df["wage"], scoring="neg_mean_squared_error", cv=10, error_score='raise')