R和Python中的广义线性模型给出了与MATLAB不同的结果

Question

我正在尝试转录一个处理从MATLAB到R和Python的广义线性模型的函​​数。 目前，R和Python都给出了相同的答案，这与MATLAB的不同，即使给出相同的输入。

MATLAB代码基本上是这样的：

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

请注意，matlab中的glmfit已经将常量项添加到X.此函数的文档位于： http ： //www.mathworks.com/help/stats/glmfit.html

在R中，我有这样的事情：

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

R中的glm文档位于： http ： //stat.ethz.ch/R-manual/R-patched/library/stats/html/glm.html

在Python中，我有这个：

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

在python中，文档在这里： http ： //statsmodels.sourceforge.net/devel/glm.html#module-reference

根据文档，所有GLM函数都使用logit参数进行link 。 如果我不得不猜测，这个问题可能归因于MATLAB的精度，这是我之前遇到过的。 （似乎MATLAB不像R或NumPy那么精确。）但我确实想确保我不仅仅使用错误的函数。

我是否认为这是MATLAB的一个问题，或者我错过了一些参数/做错了什么？

另外 - 如果它很重要，这些是我正在使用的变量（我正在从csv文件中读取）：

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

和y =

0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
1.00000
1.00000
0.00000
1.00000
1.00000
0.00000
0.00000
0.00000
1.00000
0.00000
1.00000
0.00000
0.00000
1.00000
1.00000
0.00000
1.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
1.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
1.00000
1.00000
0.00000
0.00000
1.00000
0.00000
1.00000
1.00000
0.00000
0.00000
0.00000
1.00000
1.00000
0.00000
1.00000
0.00000
1.00000
0.00000
0.00000
0.00000
0.00000
1.00000
0.00000
0.00000
1.00000
1.00000
0.00000
1.00000
1.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
1.00000
0.00000
0.00000
0.00000

感谢您的任何帮助！

Answer 1

感谢aosmith，我找到了解决方案 -

我的R代码改为：

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

我的Python代码更改为：

est = sm.GLM(np.vstack([y, 1-y]).T, sm.add_constant(X), family=sm.families.Binomial()).fit()
coeffs = est.params

谢谢！