R和Python中的广义线性模型与MATLAB结果不同

Question

我正在尝试把一个处理广义线性模型的函数从MATLAB转到R和Python。目前，R和Python给出的结果是一样的，但和MATLAB的结果不同，即使输入是相同的。

MATLAB的代码大致是这样的：

coeffs = glmfit(X, [y ones(length(y),1)], 'binomial', 'link', 'logit');

需要注意的是，MATLAB中的glmfit函数已经把常数项加到了X里面。这个函数的说明文档在这里： http://www.mathworks.com/help/stats/glmfit.html

在R中，我的代码大概是这样的：

model <- glm(cbind(y, array(1, length(y)))~X, family=binomial(link=logit))
coeffs <- model$coefficients

R中glm函数的说明文档在这里： http://stat.ethz.ch/R-manual/R-patched/library/stats/html/glm.html

在Python中，我的代码是这样的：

import statsmodels.api as sm
import numpy as np

est = sm.GLM(sm.add_constant(y, prepend=False), sm.add_constant(X), family=sm.families.Binomial()).fit()
coeffs = est.params

Python中的说明文档在这里： http://statsmodels.sourceforge.net/devel/glm.html#module-reference

根据文档，所有的GLM函数都使用logit参数作为link。如果我猜的话，这个问题可能和MATLAB的精度有关，我之前也遇到过这个问题。（似乎MATLAB的精度没有R或NumPy高。）不过，我还是想确认一下，我是不是在使用这些函数时出了什么错。

我这样想，是不是MATLAB有问题，还是我漏掉了什么参数/做错了什么？

另外，如果重要的话，这些是我使用的变量（我从一个csv文件读取）：

X =

3.00000,9.10000,0.43000,-1.26000,-0.25000,0.05000,-4.01000,7.87000
4.00000,1.70000,-1.10000,0.43000,-1.26000,-17.34000,0.05000,-4.01000
5.00000,3.80000,-0.01000,-1.10000,0.43000,5.35000,-17.34000,0.05000
6.00000,0.70000,0.13000,-0.01000,-1.10000,6.03000,5.35000,-17.34000
7.00000,5.80000,0.38000,0.13000,-0.01000,18.10000,6.03000,5.35000
8.00000,8.90000,0.13000,0.38000,0.13000,-1.88000,18.10000,6.03000
9.00000,7.60000,-0.88000,0.13000,0.38000,-7.59000,-1.88000,18.10000
10.00000,4.50000,0.01000,-0.88000,0.13000,2.67000,-7.59000,-1.88000
11.00000,2.40000,0.37000,0.01000,-0.88000,12.76000,2.67000,-7.59000
12.00000,6.60000,0.60000,0.37000,0.01000,3.25000,12.76000,2.67000
13.00000,2.80000,-1.66000,0.60000,0.37000,18.67000,3.25000,12.76000
14.00000,7.20000,1.91000,-1.66000,0.60000,-0.37000,18.67000,3.25000
15.00000,4.00000,0.78000,1.91000,-1.66000,-8.18000,-0.37000,18.67000
16.00000,7.00000,-0.81000,0.78000,1.91000,8.86000,-8.18000,-0.37000
17.00000,0.50000,0.33000,-0.81000,0.78000,-12.55000,8.86000,-8.18000
18.00000,4.00000,1.17000,0.33000,-0.81000,-10.02000,-12.55000,8.86000
19.00000,7.10000,0.20000,1.17000,0.33000,5.50000,-10.02000,-12.55000
20.00000,3.20000,0.12000,0.20000,1.17000,-20.33000,5.50000,-10.02000
3.00000,0.70000,-1.26000,-0.96000,0.88000,-12.24000,7.18000,0.31000
4.00000,1.60000,-0.70000,-1.26000,-0.96000,-1.32000,-12.24000,7.18000
5.00000,8.00000,1.98000,-0.70000,-1.26000,6.75000,-1.32000,-12.24000
6.00000,3.40000,0.80000,1.98000,-0.70000,17.24000,6.75000,-1.32000
7.00000,8.00000,-1.09000,0.80000,1.98000,-7.76000,17.24000,6.75000
8.00000,7.30000,-0.59000,-1.09000,0.80000,-2.04000,-7.76000,17.24000
9.00000,7.70000,0.69000,-0.59000,-1.09000,7.18000,-2.04000,-7.76000
10.00000,6.60000,0.09000,0.69000,-0.59000,-1.75000,7.18000,-2.04000
11.00000,0.10000,0.10000,0.09000,0.69000,1.37000,-1.75000,7.18000
12.00000,5.80000,0.18000,0.10000,0.09000,14.02000,1.37000,-1.75000
13.00000,9.90000,-1.36000,0.18000,0.10000,-3.16000,14.02000,1.37000
14.00000,1.30000,-0.26000,-1.36000,0.18000,6.47000,-3.16000,14.02000
15.00000,8.40000,-0.52000,-0.26000,-1.36000,-7.12000,6.47000,-3.16000
16.00000,7.40000,-0.66000,-0.52000,-0.26000,-1.73000,-7.12000,6.47000
17.00000,8.30000,-0.63000,-0.66000,-0.52000,11.65000,-1.73000,-7.12000
18.00000,6.70000,-1.04000,-0.63000,-0.66000,13.63000,11.65000,-1.73000
19.00000,5.80000,-1.25000,-1.04000,-0.63000,-14.71000,13.63000,11.65000
20.00000,3.20000,-1.37000,-1.25000,-1.04000,-3.60000,-14.71000,13.63000
3.00000,2.30000,-1.16000,-0.19000,-0.70000,8.41000,0.18000,-4.08000
4.00000,1.90000,1.11000,-1.16000,-0.19000,-0.00000,8.41000,0.18000
5.00000,6.40000,0.12000,1.11000,-1.16000,17.86000,-0.00000,8.41000
6.00000,3.90000,1.30000,0.12000,1.11000,1.12000,17.86000,-0.00000
7.00000,0.80000,-0.63000,1.30000,0.12000,-1.33000,1.12000,17.86000
8.00000,7.60000,-0.21000,-0.63000,1.30000,22.26000,-1.33000,1.12000
9.00000,0.90000,1.47000,-0.21000,-0.63000,-14.10000,22.26000,-1.33000
10.00000,5.10000,0.60000,1.47000,-0.21000,13.36000,-14.10000,22.26000
11.00000,6.40000,-1.41000,0.60000,1.47000,-5.37000,13.36000,-14.10000
12.00000,3.30000,-0.97000,-1.41000,0.60000,6.47000,-5.37000,13.36000
13.00000,8.80000,1.82000,-0.97000,-1.41000,8.82000,6.47000,-5.37000
14.00000,9.90000,1.80000,1.82000,-0.97000,5.63000,8.82000,6.47000
15.00000,3.40000,-0.60000,1.80000,1.82000,5.02000,5.63000,8.82000
16.00000,5.90000,-1.14000,-0.60000,1.80000,10.93000,5.02000,5.63000
17.00000,3.00000,0.77000,-1.14000,-0.60000,-2.12000,10.93000,5.02000
18.00000,1.60000,1.69000,0.77000,-1.14000,-2.89000,-2.12000,10.93000
19.00000,1.10000,-0.07000,1.69000,0.77000,-2.78000,-2.89000,-2.12000
20.00000,0.70000,-0.66000,-0.07000,1.69000,2.82000,-2.78000,-2.89000
3.00000,1.30000,-0.72000,1.12000,1.41000,4.24000,5.35000,-0.62000
4.00000,4.80000,-1.18000,-0.72000,1.12000,8.91000,4.24000,5.35000
5.00000,1.30000,-0.44000,-1.18000,-0.72000,1.15000,8.91000,4.24000
6.00000,8.90000,-0.42000,-0.44000,-1.18000,11.64000,1.15000,8.91000
7.00000,6.20000,0.06000,-0.42000,-0.44000,20.74000,11.64000,1.15000
8.00000,6.60000,1.83000,0.06000,-0.42000,21.14000,20.74000,11.64000
9.00000,2.80000,1.50000,1.83000,0.06000,-16.67000,21.14000,20.74000
10.00000,8.70000,-1.72000,1.50000,1.83000,9.86000,-16.67000,21.14000
11.00000,6.90000,-1.51000,-1.72000,1.50000,14.44000,9.86000,-16.67000
12.00000,1.80000,-1.10000,-1.51000,-1.72000,3.64000,14.44000,9.86000
13.00000,4.30000,-1.34000,-1.10000,-1.51000,13.78000,3.64000,14.44000
14.00000,4.90000,-0.31000,-1.34000,-1.10000,-2.43000,13.78000,3.64000
15.00000,2.50000,1.69000,-0.31000,-1.34000,5.85000,-2.43000,13.78000
16.00000,1.70000,0.67000,1.69000,-0.31000,-0.94000,5.85000,-2.43000
17.00000,8.00000,1.23000,0.67000,1.69000,-2.19000,-0.94000,5.85000
18.00000,1.40000,0.63000,1.23000,0.67000,14.29000,-2.19000,-0.94000
19.00000,5.00000,1.10000,0.63000,1.23000,7.65000,14.29000,-2.19000
20.00000,4.10000,-0.13000,1.10000,0.63000,3.03000,7.65000,14.29000
3.00000,3.70000,-0.79000,-1.32000,-0.62000,-5.73000,0.93000,-0.62000
4.00000,0.90000,1.56000,-0.79000,-1.32000,3.27000,-5.73000,0.93000
5.00000,6.90000,2.39000,1.56000,-0.79000,11.63000,3.27000,-5.73000
6.00000,0.20000,1.17000,2.39000,1.56000,2.61000,11.63000,3.27000
7.00000,2.30000,-0.83000,1.17000,2.39000,18.57000,2.61000,11.63000
8.00000,0.10000,0.08000,-0.83000,1.17000,2.48000,18.57000,2.61000
9.00000,0.80000,-0.52000,0.08000,-0.83000,-2.11000,2.48000,18.57000
10.00000,3.40000,0.47000,-0.52000,0.08000,-5.58000,-2.11000,2.48000
11.00000,3.30000,-1.37000,0.47000,-0.52000,-5.09000,-5.58000,-2.11000
12.00000,7.70000,-0.54000,-1.37000,0.47000,-13.45000,-5.09000,-5.58000
13.00000,7.80000,2.62000,-0.54000,-1.37000,13.67000,-13.45000,-5.09000
14.00000,3.50000,0.91000,2.62000,-0.54000,-10.03000,13.67000,-13.45000
15.00000,4.40000,-0.73000,0.91000,2.62000,7.27000,-10.03000,13.67000
16.00000,0.50000,0.53000,-0.73000,0.91000,-5.44000,7.27000,-10.03000
17.00000,4.50000,-0.80000,0.53000,-0.73000,7.60000,-5.44000,7.27000
18.00000,7.90000,0.01000,-0.80000,0.53000,-11.30000,7.60000,-5.44000
19.00000,6.30000,0.42000,0.01000,-0.80000,9.38000,-11.30000,7.60000
20.00000,2.70000,0.13000,0.42000,0.01000,3.55000,9.38000,-11.30000

y =

谢谢大家的帮助！

数据处理 matlab 参数设置 R语言精度问题统计建模广义线性模型 glm函数

R和Python中的广义线性模型与MATLAB结果不同

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