我用统计模型测试了一些基本的类别回归: 我建立了一个确定性模型
Y = X + Z
其中X可以取3个值(a、b或c),Z只能取2(d或e)。 在那个阶段,模型是完全确定的,我为每个变量设置了如下的权重
a's weight=1
b's weight=2
c's weight=3
d's weight=1
e's weight=2
因此,当1(X=a)为1时,如果X=a,则为0,否则,模型为:
Y = 1(X=a) + 2*1(X=b) + 3*1(X=c) + 1(Z=d) + 2*1(Z=e)
使用以下代码,生成不同的变量并运行回归
from statsmodels.formula.api import ols
nbData = 1000
rand1 = np.random.uniform(size=nbData)
rand2 = np.random.uniform(size=nbData)
a = 1 * (rand1 <= (1.0/3.0))
b = 1 * (((1.0/3.0)< rand1) & (rand1< (4/5.0)))
c = 1-b-a
d = 1 * (rand2 <= (3.0/5.0))
e = 1-d
weigths = [1,2,3,1,2]
y = a+2*b+3*c+4*d+5*e
df = pd.DataFrame({'y':y, 'a':a, 'b':b, 'c':c, 'd':d, 'e':e})
mod = ols(formula='y ~ a + b + c + d + e - 1', data=df)
res = mod.fit()
print(res.summary())
我最终得到了正确的结果(人们必须关注coef之间的差异,而不是coef本身)
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 1.006e+30
Date: Wed, 16 Sep 2015 Prob (F-statistic): 0.00
Time: 03:05:40 Log-Likelihood: 3156.8
No. Observations: 100 AIC: -6306.
Df Residuals: 96 BIC: -6295.
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
a 1.6000 7.47e-16 2.14e+15 0.000 1.600 1.600
b 2.6000 6.11e-16 4.25e+15 0.000 2.600 2.600
c 3.6000 9.61e-16 3.74e+15 0.000 3.600 3.600
d 3.4000 5.21e-16 6.52e+15 0.000 3.400 3.400
e 4.4000 6.85e-16 6.42e+15 0.000 4.400 4.400
==============================================================================
Omnibus: 11.299 Durbin-Watson: 0.833
Prob(Omnibus): 0.004 Jarque-Bera (JB): 5.720
Skew: -0.381 Prob(JB): 0.0573
Kurtosis: 2.110 Cond. No. 2.46e+15
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 1.67e-29. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
但当我将数据点的数量增加到(比如)600时,回归结果就非常糟糕。我在Excel和R中尝试过类似的回归,无论数据点多少,它们都会产生一致的结果。是否有人知道对解释这种行为的statsmodel ols有什么限制,或者我遗漏了什么?
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.167
Model: OLS Adj. R-squared: 0.161
Method: Least Squares F-statistic: 29.83
Date: Wed, 16 Sep 2015 Prob (F-statistic): 1.23e-22
Time: 03:08:04 Log-Likelihood: -701.02
No. Observations: 600 AIC: 1412.
Df Residuals: 595 BIC: 1434.
Df Model: 4
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
a 5.8070 1.15e+13 5.05e-13 1.000 -2.26e+13 2.26e+13
b 6.4951 1.15e+13 5.65e-13 1.000 -2.26e+13 2.26e+13
c 6.9033 1.15e+13 6.01e-13 1.000 -2.26e+13 2.26e+13
d -1.1927 1.15e+13 -1.04e-13 1.000 -2.26e+13 2.26e+13
e -0.1685 1.15e+13 -1.47e-14 1.000 -2.26e+13 2.26e+13
==============================================================================
Omnibus: 67.153 Durbin-Watson: 0.328
Prob(Omnibus): 0.000 Jarque-Bera (JB): 70.964
Skew: 0.791 Prob(JB): 3.89e-16
Kurtosis: 2.419 Cond. No. 7.70e+14
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 9.25e-28. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
正如F先生所提到的,主要的问题是statsmodel OLS在这种情况下似乎不能处理共线pb和Excel/R,但是如果不是为每个
a, b, c, d and e
定义一个变量X
和一个Z
,它们可以等于a, b or c
和d or e
,这样回归就很好了。Ie更新代码:导致预期结果
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