常用统计学回归模型应用场景与python实现方法
在信息管理、数据科学或fintech等研究中,有时会遇到统计学回归模型,那么这些基本统计回归模型的使用场景是什么?该如何用python快捷的实现统计回归呢?本文从数据类型出发对统计回归模型进行了分类整理,并基于python的statsmodel库(类R语言),给出了这些模型的一种实现方案。
一、理清数据类型:横截面数据、时间序列数据、分层数据or面板数据
为了下文表达清晰,构造一张经典表如下:
Table 1 |
2000 |
2001 |
2002 |
2000 |
2001 |
2002 |
2000 |
2001 |
2002 |
北京 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
上海 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
天津 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
- 横截面数据:同一时间,不同统计单位相同统计指标组成的数据列,按照统计单位排列。如:
Table 2 |
2000 |
北京 |
9 |
上海 |
8 |
天津 |
5 |
- 时间序列数据:某事物、现象随时间的变化状态,即它在不同时间点的数据。如:
Table 3 |
2000 |
2001 |
2002 |
2000 |
2001 |
北京 |
9 |
10 |
11 |
12 |
13 |
- 分层数据: 不仅有描述个体的变量,而且有个人组成的更高一层的变量(可以包括若干层具有层次结构的变量)。如Table 4:
省 |
区 |
2000 |
2001 |
2002 |
2000 |
北京 |
海淀 |
2 |
3 |
4 |
5 |
北京 |
朝阳 |
1 |
2 |
3 |
4 |
- 面板数据: 由截面数据和时间序列数据综合而来的数据类型。如Table 1所示。
二、明确因变量类型:连续变量、计数变量、分类变量
- 连续变量:数值是连续不断的
- 计数变量:变量值只能取非负整数{0,1,2,3,...}。这个变量来自计数(count)而非排名。
- 分类变量:变量值是定性的,表现为互不相容的类别或属性。如类别1、属性2。分为无需变量和有序变量两类。
三、选择统计回归模型:
四、常用回归模型的python实现:
- 使用http://www.scipy-lectures.org/_downloads/brain_size.csv脑容量数据举例,样例如下:
![常用统计学回归模型应用场景与python实现方法_第2张图片](http://img.e-com-net.com/image/info8/1453360c94814603a6493b2523287a7e.png)
![]()
- 1、利用pandas读取数据并保存成dataframe:
import pandas
data = pandas.read_csv('brain_size.csv', sep=';', na_values=".")
- 2、利用线性模型比较男女IQ值(其中类别"Gender"被自动识别为分类变量)
model = ols("VIQ ~ Gender + 1", data).fit()
print(model.summary())
OLS Regression Results
==============================================================================
Dep. Variable: VIQ R-squared: 0.015
Model: OLS Adj. R-squared: -0.010
Method: Least Squares F-statistic: 0.5969
Date: Tue, 09 May 2017 Prob (F-statistic): 0.445
Time: 17:45:59 Log-Likelihood: -182.42
No. Observations: 40 AIC: 368.8
Df Residuals: 38 BIC: 372.2
Df Model: 1
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
Intercept 109.4500 5.308 20.619 0.000 98.704 120.196
Gender[T.Male] 5.8000 7.507 0.773 0.445 -9.397 20.997
==============================================================================
Omnibus: 26.188 Durbin-Watson: 1.709
Prob(Omnibus): 0.000 Jarque-Bera (JB): 3.703
Skew: 0.010 Prob(JB): 0.157
Kurtosis: 1.510 Cond. No. 2.62
==============================================================================
- 3、线性多元回归模型探究体重、身高、性别对IQ值(连续值)的影响
model = ols('VIQ ~ Gender + Weight + Height', data).fit()
print(model.summary())
OLS Regression Results
==============================================================================
Dep. Variable: VIQ R-squared: 0.108
Model: OLS Adj. R-squared: 0.029
Method: Least Squares F-statistic: 1.369
Date: Tue, 09 May 2017 Prob (F-statistic): 0.269
Time: 17:52:24 Log-Likelihood: -170.29
No. Observations: 38 AIC: 348.6
Df Residuals: 34 BIC: 355.1
Df Model: 3
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
Intercept 261.8374 88.157 2.970 0.005 82.680 440.995
Gender[T.Male] 20.4303 10.822 1.888 0.068 -1.562 42.423
Weight -0.1012 0.230 -0.441 0.662 -0.568 0.366
Height -2.1059 1.490 -1.414 0.167 -5.134 0.922
==============================================================================
Omnibus: 7.582 Durbin-Watson: 2.159
Prob(Omnibus): 0.023 Jarque-Bera (JB): 2.540
Skew: -0.231 Prob(JB): 0.281
Kurtosis: 1.820 Cond. No. 4.03e+03
==============================================================================
- 4、利用medpar数据集进行负二项式回归例子(因变量为计数变量)
数据样例:
los hmo white died age80 type type1 type2 type3 provnum
0 4 0 1 0 0 1 1 0 0 30001
1 9 1 1 0 0 1 1 0 0 30001
2 3 1 1 1 1 1 1 0 0 30001
3 9 0 1 0 0 1 1 0 0 30001
4 1 0 1 1 1 1 1 0 0 30001
#example for Negative Binomial Regression for Count Data
medpar = sm.datasets.get_rdataset("medpar", "COUNT", cache=True).data
y = medpar.los
X = medpar[["type2", "type3", "hmo", "white"]].copy()
X["constant"] = 1
res_nbin = NegativeBinomial(y, X).fit(disp=0)
print(res_nbin.summary())
NegativeBinomial Regression Results
==============================================================================
Dep. Variable: los No. Observations: 1495
Model: NegativeBinomial Df Residuals: 1490
Method: MLE Df Model: 4
Date: Tue, 09 May 2017 Pseudo R-squ.: 0.01215
Time: 18:13:53 Log-Likelihood: -4797.5
converged: True LL-Null: -4856.5
LLR p-value: 1.404e-24
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
type2 0.2212 0.051 4.373 0.000 0.122 0.320
type3 0.7062 0.076 9.276 0.000 0.557 0.855
hmo -0.0680 0.053 -1.277 0.202 -0.172 0.036
white -0.1291 0.069 -1.883 0.060 -0.263 0.005
constant 2.3103 0.068 34.001 0.000 2.177 2.443
alpha 0.4458 0.020 22.495 0.000 0.407 0.485
==============================================================================
- 5、利用medpar数据集进行Poisson回归例子
#poisson regression model
poisson = Poisson(y, X).fit()
print(poisson.summary())
Optimization terminated successfully.
Current function value: 4.634721
Iterations 21
Poisson Regression Results
==============================================================================
Dep. Variable: los No. Observations: 1495
Model: Poisson Df Residuals: 1490
Method: MLE Df Model: 4
Date: Tue, 09 May 2017 Pseudo R-squ.: 0.05189
Time: 18:21:46 Log-Likelihood: -6928.9
converged: True LL-Null: -7308.1
LLR p-value: 7.600e-163
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
type2 0.2217 0.021 10.529 0.000 0.180 0.263
type3 0.7095 0.026 27.146 0.000 0.658 0.761
hmo -0.0715 0.024 -2.988 0.003 -0.118 -0.025
white -0.1539 0.027 -5.613 0.000 -0.208 -0.100
constant 2.3329 0.027 85.744 0.000 2.280 2.386
==============================================================================
、
更多模型,可自行参考python statsmodels doc: http://www.statsmodels.org/stable/。
参考:
- 常用回归模型:https://wenku.baidu.com/view/1b124799daef5ef7ba0d3cee.html
- http://www.scipy-lectures.org/packages/statistics/index.html
- http://www.statsmodels.org/stable/
- python中的统计学:https://wizardforcel.gitbooks.io/scipy-lecture-notes/content/14.html