R和Python中的廣義線性模型給出了與MATLAB不同的結果

Question

我正在嘗試轉錄一個處理從MATLAB到R和Python的廣義線性模型的函​​數。 目前，R和Python都給出了相同的答案，這與MATLAB的不同，即使給出相同的輸入。

MATLAB代碼基本上是這樣的：

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

請注意，matlab中的glmfit已經將常量項添加到X.此函數的文檔位於： http ： //www.mathworks.com/help/stats/glmfit.html

在R中，我有這樣的事情：

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

R中的glm文檔位於： http ： //stat.ethz.ch/R-manual/R-patched/library/stats/html/glm.html

在Python中，我有這個：

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，文檔在這里： http ： //statsmodels.sourceforge.net/devel/glm.html#module-reference

根據文檔，所有GLM函數都使用logit參數進行link 。 如果我不得不猜測，這個問題可能歸因於MATLAB的精度，這是我之前遇到過的。 （似乎MATLAB不像R或NumPy那么精確。）但我確實想確保我不僅僅使用錯誤的函數。

我是否認為這是MATLAB的一個問題，或者我錯過了一些參數/做錯了什么？

另外 - 如果它很重要，這些是我正在使用的變量（我正在從csv文件中讀取）：

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

感謝您的任何幫助！

Answer 1

感謝aosmith，我找到了解決方案 -

我的R代碼改為：

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

我的Python代碼更改為：

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

謝謝！