在 python 中估计模型的多个参数

Question

想知道在模型中用 Python 估计这些参数 (a0, a1, a2, a3) 的最 efficient/accurate 方法是什么：

col_4 = a0 + a1*col_1 + a2*col_2 + a3*col_3

示例数据集为：

inputs = {
    'col_1': np.random.normal(15,2,100),
    'col_2': np.random.normal(15,1,100),
    'col_3': np.random.normal(0.9,1,100),
    'col_4': np.random.normal(-0.05,0.5,100),
}

_idx = pd.date_range('2021-01-01','2021-04-10',freq='D').to_series()
data = pd.DataFrame(inputs, index = _idx)

Answer 1

statsmodels 提供了一种非常简单的方法来估计这样的线性模型：

import statsmodels.formula.api as smf

results = smf.ols('col_4 ~ col_1 + col_2 + col_3', data=data).fit()
print(results.summary())

coef 列显示您的 aX 参数：

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  col_4   R-squared:                       0.049
Model:                            OLS   Adj. R-squared:                  0.019
Method:                 Least Squares   F-statistic:                     1.637
Date:                Wed, 29 Dec 2021   Prob (F-statistic):              0.186
Time:                        17:25:00   Log-Likelihood:                -68.490
No. Observations:                 100   AIC:                             145.0
Df Residuals:                      96   BIC:                             155.4
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      0.2191      0.846      0.259      0.796      -1.461       1.899
col_1         -0.0198      0.023     -0.854      0.395      -0.066       0.026
col_2         -0.0048      0.051     -0.093      0.926      -0.107       0.097
col_3          0.1155      0.056      2.066      0.042       0.005       0.226
==============================================================================
Omnibus:                        2.292   Durbin-Watson:                   2.291
Prob(Omnibus):                  0.318   Jarque-Bera (JB):                2.296
Skew:                          -0.351   Prob(JB):                        0.317
Kurtosis:                       2.757   Cond. No.                         370.
==============================================================================

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

默认情况下包括拦截 (a0)。如果要去掉，只需要在公式

中加一个-1

在 python 中估计模型的多个参数

Estimating multiple parameters of a model in python

python

statistics

regression

statsmodels