python statsmodels：输出差异 "formula.api" 与“"regression.quantile_regression"

Question

对于使用 python 的模块 statsmodels，我想知道使用 statsmodels.formula.api 与 statsmodels.regression.quantile_regression 调用相同过程的差异是如何产生的。特别是，我获得了参数估计的差异。

附上一个最小工作示例。

#%% Moduls;
import numpy as np
import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.regression.quantile_regression import QuantReg


#%% Load in sample data;
data = sm.datasets.engel.load_pandas().data

#%% smf-Version;
model1 = smf.quantreg(formula='foodexp ~ income', data=data, missing="drop")
result1 = model1.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)

#%% QuantReg-Version;
model2 = QuantReg \
    (
        data['foodexp'].values,
        exog            =           sm.tools.tools.add_constant(data['income']).values,
        missing         =           'drop'
    )
result2 = model2.fit \
    (
        q              =           0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06
    )

#%% Compare Results;
print(result1.params[0])
print(result2.params[0])
print('Difference times 10^9:       ' + str(abs(10**9*(result1.params[0]-result2.params[0]))))

编辑：

我需要编辑我的问题；我仍然非常感谢下面提出的解决方法，但在应用设置中不起作用；原因：我没有只有 1 个回归量。请查找附件中的修改版本。

#%% Moduls;
import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.regression.quantile_regression import QuantReg


#%% Load in sample data;
data = sm.datasets.engel.load_pandas().data
data['income2'] = data['income']**2

#%% smf-Version;
model1 = smf.quantreg(formula='foodexp ~ income + income2', data=data, missing="drop")
result1 = model1.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)

#%% QuantReg-Version;
model2 = QuantReg \
    (
        data['foodexp'].values,
        exog            =           sm.tools.tools.add_constant(data[['income', 'income2']].values),
        missing         =           'drop'
    )
result2 = model2.fit \
    (
        q              =           0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06
    )

#%% Compare Results;
print(result1.params[0])
print(result2.params[0])
print('Difference times 10^9:       ' + str(abs(10**9*(result1.params[0]-result2.params[0]))))

Answer 1

您需要对代码稍作改动。这有很大的不同

#%% QuantReg-Version;
model2 = QuantReg ( data['foodexp'].values, exog = sm.tools.tools.add_constant(data['income'].values), missing = 'drop')

当你把它放在外面时，在内部实现上有很大的不同。

最终实施

    #%% Moduls;
    import numpy as np
    import pandas as pd
    import statsmodels.api as sm
    import statsmodels.formula.api as smf
    from statsmodels.regression.quantile_regression import QuantReg


    #%% Load in sample data;
    data = sm.datasets.engel.load_pandas().data

    #%% smf-Version;
    model1 = smf.quantreg(formula='foodexp ~ income', data=data, missing="drop")
    result1 = model1.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', 
    max_iter=1000, p_tol=1e-06)

    #%% QuantReg-Version;
    model2 = QuantReg \
        (
            data['foodexp'].values,
            exog  =   sm.tools.tools.add_constant(data['income'].values),
            missing  = "drop"
        )
    result2 = model2.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)

    #%% Compare Results;
    print(result1.params[0])
    print(result2.params[0])
    print('Difference times 10^9:       ' + str(abs(10**9*(result1.params[0]-result2.params[0]))))

除了我上面的代码。我已将 exog 从模型 2 复制到模型 1

    #%% Moduls;
import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.regression.quantile_regression import QuantReg


#%% Load in sample data;
data = sm.datasets.engel.load_pandas().data
data['income2'] = data['income']**2

model1 = smf.quantreg(formula='foodexp ~ income + income2', data=data, missing="drop")
model2 = QuantReg (data['foodexp'].values, exog = sm.tools.tools.add_constant(data[['income', 'income2']].values), missing = 'drop')
model1.exog = model2.exog 

result1 = model1.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)
result2 = model2.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)

#%% Compare Results;
print(result1.params[0])
print(result2.params[0])
print('Difference times 10^9:       ' + str(abs(10**9*(result1.params[0]-result2.params[0]))))

第二种方法：- 我已将 exog 从模型 1 复制到模型 2

#%% Moduls;
import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.regression.quantile_regression import QuantReg


#%% Load in sample data;
data = sm.datasets.engel.load_pandas().data
data['income2'] = data['income']**2

model1 = smf.quantreg(formula='foodexp ~ income + income2', data=data, missing="drop")
model2 = QuantReg (data['foodexp'].values, exog = sm.tools.tools.add_constant(data[['income', 'income2']].values), missing = 'drop')
model2.exog = model1.exog 

result1 = model1.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)
result2 = model2.fit(q=0.5, vcov='robust', kernel='epa', bandwidth='hsheather', max_iter=1000, p_tol=1e-06)

#%% Compare Results;
print(result1.params[0])
print(result2.params[0])
print('Difference times 10^9:       ' + str(abs(10**9*(result1.params[0]-result2.params[0]))))

如果我将两个 exog 保持为相同的值，则答案是相等的。因此，我之前提到的数据转换的实现存在明显差异。

python statsmodels：输出差异 "formula.api" 与“"regression.quantile_regression"

python statsmodels: Difference in output "formula.api" vs. ""regression.quantile_regression"

python

api

statsmodels

quantile-regression