Regression.quantile_regression统计模型:输出"formula.api“与”“python”“的差异

Question

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

附上了一个最小的工作示例。

#%% 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；下面提出的解决方法，我仍然非常感谢，在应用的设置中不起作用；原因:我没有只有1个回归器。请找到附件中的修改版本。

#%% 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

你需要在你的代码中做一点小小的改变。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')

当你把它放在外面的时候，会在内部实现中产生很大的不同。

最终实现

    #%% 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。我已经将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]))))

如果我保持两个exog的值相同，那么答案是相等的。所以在我前面提到的数据转换的实现上有明显的不同。