[英]what is the difference between statsmodels.api.sm.OLS and statsmodels.formula.api.ols
[英]difference of summary between sklearn and statsmodels OLS
目标是检测并修复为什么我的 sklearn“摘要”实现之间的报告与OLS
statsmodels 的结果不匹配。 唯一匹配的是贝塔系数。
import pandas as pd
import numpy as np
from statsmodels.regression.linear_model import OLS
from sklearn import linear_model
from scipy.stats import t
class LinearRegression(linear_model.LinearRegression):
"""
LinearRegression class after sklearn's, but calculate t-statistics
and p-values for model coefficients (betas).
Additional attributes available after .fit()
are `t` and `p` which are of the shape (y.shape[1], X.shape[1])
which is (n_features, n_coefs)
This class sets the intercept to 0 by default, since usually we include it
in X.
"""
def __init__(self, *args, **kwargs):
if not "fit_intercept" in kwargs:
kwargs['fit_intercept'] = False
super(LinearRegression, self)\
.__init__(*args, **kwargs)
def fit(self, X, y, n_jobs=1):
self = super(LinearRegression, self).fit(X, y, n_jobs)
# std errors
uhat = (y-(X@self.coef_).ravel())
k = np.shape(X)[1]
s2 = (uhat.T@uhat)/(y.shape[0])
var = s2*np.linalg.inv(X.T@X)
self.se = np.sqrt(np.diag(var))
# T-Stat
self.t_stats = self.coef_/self.se
# p-values
self.df = y.shape[0] - k # -1 degrees of freedom: N minus number of parameters
self.p_values = 2*(t.sf(abs(self.t_stats),self.df))
# Rsquared
tss = (y-np.mean(y)).T@(y-np.mean(y))
rss = uhat.T@uhat
self.rsq = 1 - rss/tss
self.summary = pd.DataFrame({
"beta":self.coef_.reshape(1,-1).tolist()[0],
"se":self.se.reshape(1,-1).tolist()[0],
"t_stats":self.t_stats.reshape(1,-1).tolist()[0],
"p_values":self.p_values.reshape(1,-1).tolist()[0],
})
return self
在玩具数据集中运行 function 我们可以测试结果:
import statsmodels.api as sm
data = sm.datasets.longley.load_pandas()
# Estimate statsmodels OLS
model = OLS(endog=data.endog,exog=data.exog).fit()
# Estimate Sklearn with report like statsmodels OLS
model2 = LinearRegression(fit_intercept=False).fit(data.exog,np.array(data.endog))
model2.summary
我担心某些公式与正确的公式不匹配。
这里有一个 class,您可以使用它来使用 Scikit-learn 获得 LinearRegression model 摘要:
import numpy as np
import pandas as pd
from scipy.stats import t
from sklearn import linear_model
class LinearRegression(linear_model.LinearRegression):
def __init__(self, *args, **kwargs):
if not "fit_intercept" in kwargs:
self.with_intercept = True
kwargs['fit_intercept'] = True
else:
self.with_intercept = False
kwargs['fit_intercept'] = False
super(LinearRegression, self).__init__(*args, **kwargs)
def fit(self, X, y):
self = super(LinearRegression, self).fit(X, y)
y_pred = self.predict(X)
residuals = y - y_pred
residual_sum_of_squares = residuals.T @ residuals
if self.with_intercept:
coefficients = [coef for coef in self.coef_]
self.coefficients = [self.intercept_] + coefficients
p = len(X.columns) + 1 # plus one because an intercept is added
new_X = np.empty(shape=(len(X), p), dtype=float)
new_X[:, 0] = 1
new_X[:, 1:p] = X.values
else:
self.coefficients = self.coef_
p = len(X.columns)
new_X = X.values
# standard errors
sigma_squared_hat = residual_sum_of_squares / (len(X) - p)
var_beta_hat = np.linalg.inv(new_X.T @ new_X) * sigma_squared_hat
self.std_errors = [var_beta_hat[p_, p_] ** 0.5 for p_ in range(p)]
# t_values
self.t_values = np.array(self.coefficients)/self.std_errors
# p values
freedom_degree = y.shape[0] - X.shape[1]
self.p_values = 2*(t.sf(abs(self.t_values), freedom_degree))
# summary
self.summary = pd.DataFrame()
self.summary['Coefficients'] = self.coefficients
self.summary['Standard errors'] = self.std_errors
self.summary['t values'] = self.t_values
self.summary['p values'] = self.p_values
return self
这是您可以尝试 class 并适合 model 的方法:
import statsmodels.api as sm
data = sm.datasets.longley.load_pandas()
X = pd.DataFrame(data.exog)
y = np.array(data.endog)
# in case you want to ignore the intercept include fit_intercept=False as a parameter
model_linear_regression = LinearRegression().fit(X, y)
model_linear_regression.summary
结果:
Coefficients Standard errors t values p values
0 -3.482259e+06 890420.379 -3.911 0.003
1 1.506190e+01 84.915 0.177 0.863
2 -3.580000e-02 0.033 -1.070 0.310
3 -2.020200e+00 0.488 -4.136 0.002
4 -1.033200e+00 0.214 -4.822 0.001
5 -5.110000e-02 0.226 -0.226 0.826
6 1.829151e+03 455.478 4.016 0.002
您可以训练一个 OLS model,在您想要添加截距/常量的情况下进行必要的更改,如下所示:
with_intercept = True
if with_intercept:
p = len(X.columns) + 1 # plus one because an intercept is added
new_X = np.empty(shape=(len(X), p), dtype=float)
new_X[:, 0] = 1
new_X[:, 1:p] = X.values
model_statsmodel = sm.OLS(endog=y, exog=new_X).fit()
else:
model_statsmodel = sm.OLS(endog=y, exog=X).fit()
最后,您可以通过以下方式验证结果是否相同:
assert np.allclose(np.round(model_statsmodel.params, 3), np.round(model_linear_regression.coefficients, 3))
assert np.allclose(np.round(model_statsmodel.bse, 3), np.round(model_linear_regression.std_errors, 3))
assert np.allclose(np.round(model_statsmodel.tvalues, 3), np.round(model_linear_regression.t_values, 3))
# the following assertion might return False, due to a difference in the number of decimals
assert np.allclose(np.round(model_statsmodel.pvalues, 3), np.round(model_linear_regression.p_values, 3))
希望对您有所帮助:)
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