python - statsmodels.api.sm.OLS 和 statsmodels.formula.api.ols 有什么区别

Question

我用python处理一个线性回归模型，json数据如下:

{"Y":[1,2,3,4,5],"X":[[1,43,23],[2,3,43],[3,23,334],[4,43,23],[232,234,24]]}

我使用的是statsmodels.api.sm.OLS().fit和statsmodels.formula.api.ols.fit()，我认为它们是相同的模型，但结果不同。

这是第一个函数:

import statsmodels.api as sm
def analyze1():
    print 'using sm.OLS().fit'
    data = json.load(open(FNAME_DATA))
    X = np.asarray(data['X'])
    Y = np.log(np.asarray(data['Y']) + 1)
    X2 = sm.add_constant(X)
    results = sm.OLS(Y, X2).fit()
    print results.summary()

这是第二个功能:

from statsmodels.formula.api import ols
def analyze2():
    print 'using ols().fit'
    data = json.load(open(FNAME_DATA))
    results=ols('Y~X+1',data=data).fit()
    print results.summary()

第一个函数输出:

using sm.OLS().fit
/home/aaron/anaconda2/lib/python2.7/site-packages/statsmodels/stats/stattools.py:72: ValueWarning: omni_normtest is not valid with less than 8 observations; 5 samples were given.
  "samples were given." % int(n), ValueWarning)
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.449
Model:                            OLS   Adj. R-squared:                 -1.204
Method:                 Least Squares   F-statistic:                    0.2717
Date:                Wed, 07 Aug 2019   Prob (F-statistic):              0.849
Time:                        07:17:00   Log-Likelihood:               -0.87006
No. Observations:                   5   AIC:                             9.740
Df Residuals:                       1   BIC:                             8.178
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          1.0859      0.720      1.509      0.373      -8.057      10.228
x1             0.0024      0.018      0.134      0.915      -0.229       0.234
x2             0.0005      0.020      0.027      0.983      -0.256       0.257
x3             0.0008      0.003      0.332      0.796      -0.031       0.033
==============================================================================
Omnibus:                          nan   Durbin-Watson:                   1.485
Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.077
Skew:                           0.175   Prob(JB):                        0.962
Kurtosis:                       2.503   Cond. No.                         402.
==============================================================================

第二个函数输出:

using ols().fit
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      Y   R-squared:                       0.551
Model:                            OLS   Adj. R-squared:                 -0.796
Method:                 Least Squares   F-statistic:                    0.4092
Date:                Wed, 07 Aug 2019   Prob (F-statistic):              0.784
Time:                        07:17:00   Log-Likelihood:                -6.8251
No. Observations:                   5   AIC:                             21.65
Df Residuals:                       1   BIC:                             20.09
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      1.9591      2.368      0.827      0.560     -28.124      32.042
X[0]           0.0030      0.060      0.051      0.968      -0.757       0.764
X[1]           0.0098      0.066      0.148      0.906      -0.834       0.854
X[2]           0.0024      0.008      0.289      0.821      -0.103       0.108
==============================================================================
Omnibus:                          nan   Durbin-Watson:                   1.485
Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.077
Skew:                           0.175   Prob(JB):                        0.962
Kurtosis:                       2.503   Cond. No.                         402.
==============================================================================

我认为这些是相似的模型，但是使用相同的数据结果(coef)和对数似然不同，我不知道这两个模型是否有一些差异。

Answer 1

前者( OLS )是一个类。后者( ols )是 OLS 的一种方法从 statsmodels.base.model.Model 继承的类.

In [11]: from statsmodels.api import OLS                                           

In [12]: from statsmodels.formula.api import ols                                   

In [13]: OLS                                                                       
Out[13]: statsmodels.regression.linear_model.OLS

In [14]: ols                                                                       
Out[14]: <bound method Model.from_formula of <class 'statsmodels.regression.linear_model.OLS'>>

根据我自己的测试，我相信模型应该产生相同的结果。然而， 在您的示例中，您将 log 应用于第一个模型中的 y ，但不在第二个模型中。 相同的字段仅从 X 计算，这在两个模型中都是相同的。不同的字段是 y 不同的结果。

由于我无权访问您的数据，请随意使用此独立示例作为完整性检查。这两个模型(看起来很垃圾)在我安装它们后产生了相同的摘要。

示例:

import pandas as pd
import statsmodels.api as sm
import numpy as np
from sklearn.datasets import load_diabetes
from statsmodels.formula.api import ols

X = pd.DataFrame(data=load_diabetes()['data'],
                 columns=load_diabetes()['feature_names'])
X.drop(['age', 'bp', 's1', 's2', 's3', 's4', 's5', 's6'], axis=1, inplace=True)
X = sm.add_constant(X)
y = pd.DataFrame(data=load_diabetes()['target'], columns=['y'])

mod1 = sm.OLS(np.log(y), X)
results1 = mod1.fit()
print(results1.summary())

mod2 = ols('np.log(y) ~ sex + bmi', data=pd.concat([X, y], axis=1))
results2 = mod2.fit()
print(results2.summary())

输出 (OLS):

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.297
Model:                            OLS   Adj. R-squared:                  0.294
Method:                 Least Squares   F-statistic:                     92.90
Date:                Tue, 06 Aug 2019   Prob (F-statistic):           2.27e-34
Time:                        21:06:21   Log-Likelihood:                -291.29
No. Observations:                 442   AIC:                             588.6
Df Residuals:                     439   BIC:                             600.9
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const          4.8813      0.022    218.671      0.000       4.837       4.925
sex           -0.0868      0.471     -0.184      0.854      -1.013       0.839
bmi            6.4042      0.471     13.593      0.000       5.478       7.330
==============================================================================
Omnibus:                       14.733   Durbin-Watson:                   1.892
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               15.547
Skew:                          -0.446   Prob(JB):                     0.000421
Kurtosis:                       2.776   Cond. No.                         22.0
==============================================================================

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

输出(ols):

                            OLS Regression Results                            
==============================================================================
Dep. Variable:              np.log(y)   R-squared:                       0.297
Model:                            OLS   Adj. R-squared:                  0.294
Method:                 Least Squares   F-statistic:                     92.90
Date:                Wed, 27 May 2020   Prob (F-statistic):           2.27e-34
Time:                        01:42:40   Log-Likelihood:                -291.29
No. Observations:                 442   AIC:                             588.6
Df Residuals:                     439   BIC:                             600.9
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      4.8813      0.022    218.671      0.000       4.837       4.925
sex           -0.0868      0.471     -0.184      0.854      -1.013       0.839
bmi            6.4042      0.471     13.593      0.000       5.478       7.330
==============================================================================
Omnibus:                       14.733   Durbin-Watson:                   1.892
Prob(Omnibus):                  0.001   Jarque-Bera (JB):               15.547
Skew:                          -0.446   Prob(JB):                     0.000421
Kurtosis:                       2.776   Cond. No.                         22.0
==============================================================================

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