r - 在 Stata 中从 R 复制结果 - 告诉 R 或 Stata 删除导致完美共线性/奇点的相同变量
问题描述
我正在尝试在 Stata 中重现 R 的结果（请注意，以下数据是虚构的，仅作为示例）。然而，出于某种原因，Stata 处理某些问题的方式似乎与 R 不同。它选择不同的虚拟变量来排除多重共线性。
我已经发布了一个相关的问题，处理这些国家年份虚拟变量在此处被删除的统计意义。
在下面的示例中，R 踢出 2，而 Stata 踢出 3，导致不同的结果。例如，检查和 的系数和votep值vote_won。
本质上，我只想知道如何与 R 或 Stata 通信，哪些变量要踢出，以便它们都做同样的事情。
数据
数据如下所示：
library(data.table)
library(dplyr)
library(foreign)
library(censReg)
library(wooldridge)
data('mroz')
year= c(2005, 2010)
country = c("A", "B", "C", "D", "E", "F", "G", "H", "I", "J")
n <- 2
DT <- data.table( country = rep(sample(country, length(mroz), replace = T), each = n),
year = c(replicate(length(mroz), sample(year, n))))
x <- DT
DT <- rbind(DT, DT); DT <- rbind(DT, DT); DT <- rbind(DT, DT) ; DT <- rbind(DT, DT); DT <- rbind(DT, x)
mroz <- mroz[-c(749:753),]
DT <- cbind(mroz, DT)
DT <- DT %>%
group_by(country) %>%
mutate(base_rate = as.integer(runif(1, 12.5, 37.5))) %>%
group_by(country, year) %>%
mutate(taxrate = base_rate + as.integer(runif(1,-2.5,+2.5)))
DT <- DT %>%
group_by(country, year) %>%
mutate(vote = sample(c(0,1),1),
votewon = ifelse(vote==1, sample(c(0,1),1),0))
rm(mroz,x, country, year)
R中的lm回归
summary(lm(educ ~ exper + I(exper^2) + vote + votewon + country:as.factor(year), data=DT))
Call:
lm(formula = educ ~ exper + I(exper^2) + vote + votewon + country:as.factor(year),
data = DT)
Residuals:
Min 1Q Median 3Q Max
-7.450 -0.805 -0.268 0.954 5.332
Coefficients: (3 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.170064 0.418578 26.69 < 0.0000000000000002 ***
exper 0.103880 0.029912 3.47 0.00055 ***
I(exper^2) -0.002965 0.000966 -3.07 0.00222 **
vote 0.576865 0.504540 1.14 0.25327
votewon 0.622522 0.636241 0.98 0.32818
countryA:as.factor(year)2005 -0.196348 0.503245 -0.39 0.69653
countryB:as.factor(year)2005 -0.530681 0.616653 -0.86 0.38975
countryC:as.factor(year)2005 0.650166 0.552019 1.18 0.23926
countryD:as.factor(year)2005 -0.515195 0.638060 -0.81 0.41968
countryE:as.factor(year)2005 0.731681 0.502807 1.46 0.14605
countryG:as.factor(year)2005 0.213345 0.674642 0.32 0.75192
countryH:as.factor(year)2005 -0.811374 0.637254 -1.27 0.20334
countryI:as.factor(year)2005 0.584787 0.503606 1.16 0.24594
countryJ:as.factor(year)2005 0.554397 0.674789 0.82 0.41158
countryA:as.factor(year)2010 0.388603 0.503358 0.77 0.44035
countryB:as.factor(year)2010 -0.727834 0.617210 -1.18 0.23869
countryC:as.factor(year)2010 -0.308601 0.504041 -0.61 0.54056
countryD:as.factor(year)2010 0.785603 0.503165 1.56 0.11888
countryE:as.factor(year)2010 0.280305 0.452293 0.62 0.53562
countryG:as.factor(year)2010 0.672074 0.674721 1.00 0.31954
countryH:as.factor(year)2010 NA NA NA NA
countryI:as.factor(year)2010 NA NA NA NA
countryJ:as.factor(year)2010 NA NA NA NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.3 on 728 degrees of freedom
Multiple R-squared: 0.037, Adjusted R-squared: 0.0119
F-statistic: 1.47 on 19 and 728 DF, p-value: 0.0882
Stata中的相同回归
write.dta(DT, "C:/Users/.../mroz_adapted.dta")
encode country, gen(n_country)
reg educ c.exper c.exper#c.exper vote votewon n_country#i.year
note: 9.n_country#2010.year omitted because of collinearity
note: 10.n_country#2010.year omitted because of collinearity
Source | SS df MS Number of obs = 748
-------------+---------------------------------- F(21, 726) = 1.80
Model | 192.989406 21 9.18997171 Prob > F = 0.0154
Residual | 3705.47583 726 5.1039612 R-squared = 0.0495
-------------+---------------------------------- Adj R-squared = 0.0220
Total | 3898.46524 747 5.21882897 Root MSE = 2.2592
---------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------+----------------------------------------------------------------
exper | .1109858 .0297829 3.73 0.000 .052515 .1694567
|
c.exper#c.exper | -.0031891 .000963 -3.31 0.001 -.0050796 -.0012986
|
vote | .0697273 .4477115 0.16 0.876 -.8092365 .9486911
votewon | -.0147825 .6329659 -0.02 0.981 -1.257445 1.227879
|
n_country#year |
A#2010 | .0858634 .4475956 0.19 0.848 -.7928728 .9645997
B#2005 | -.4950677 .5003744 -0.99 0.323 -1.477421 .4872858
B#2010 | .0951657 .5010335 0.19 0.849 -.8884818 1.078813
C#2005 | -.5162827 .447755 -1.15 0.249 -1.395332 .3627664
C#2010 | -.0151834 .4478624 -0.03 0.973 -.8944434 .8640767
D#2005 | .3664596 .5008503 0.73 0.465 -.6168283 1.349747
D#2010 | .5119858 .500727 1.02 0.307 -.4710599 1.495031
E#2005 | .5837942 .6717616 0.87 0.385 -.7350329 1.902621
E#2010 | .185601 .5010855 0.37 0.711 -.7981486 1.169351
F#2005 | .5987978 .6333009 0.95 0.345 -.6445219 1.842117
F#2010 | .4853639 .7763936 0.63 0.532 -1.038881 2.009608
G#2005 | -.3341302 .6328998 -0.53 0.598 -1.576663 .9084021
G#2010 | .2873193 .6334566 0.45 0.650 -.956306 1.530945
H#2005 | -.4365233 .4195984 -1.04 0.299 -1.260294 .3872479
H#2010 | -.1683725 .6134262 -0.27 0.784 -1.372673 1.035928
I#2005 | -.39264 .7755549 -0.51 0.613 -1.915238 1.129958
I#2010 | 0 (omitted)
J#2005 | 1.036108 .4476018 2.31 0.021 .1573591 1.914856
J#2010 | 0 (omitted)
|
_cons | 11.58369 .350721 33.03 0.000 10.89514 12.27224
---------------------------------------------------------------------------------
解决方案
仅针对您关于“要排除哪些变量”的问题：我猜您的意思是要使用哪种交互项组合作为计算回归系数的参考组。
默认情况下，Stata 使用两个变量的最小值的组合作为参考，而 R 使用两个变量的最大值作为参考。我使用Stataauto数据来证明这一点：
# In R
webuse::webuse("auto")
auto$foreign = as.factor(auto$foreign)
auto$rep78 = as.factor(auto$rep78)
# Model
r_model <- lm(mpg ~ rep78:foreign, data=auto)
broom::tidy(r_model)
# A tibble: 11 x 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 26.3 1.65 15.9 2.09e-23
2 rep781:foreign0 -5.33 3.88 -1.38 1.74e- 1
3 rep782:foreign0 -7.21 2.41 -2.99 4.01e- 3
4 rep783:foreign0 -7.33 1.91 -3.84 2.94e- 4
5 rep784:foreign0 -7.89 2.34 -3.37 1.29e- 3
6 rep785:foreign0 5.67 3.88 1.46 1.49e- 1
7 rep781:foreign1 NA NA NA NA
8 rep782:foreign1 NA NA NA NA
9 rep783:foreign1 -3.00 3.31 -0.907 3.68e- 1
10 rep784:foreign1 -1.44 2.34 -0.618 5.39e- 1
11 rep785:foreign1 NA NA NA NA
在Stata中：
. reg mpg i.foreign#i.rep78
note: 1.foreign#1b.rep78 identifies no observations in the sample
note: 1.foreign#2.rep78 identifies no observations in the sample
Source | SS df MS Number of obs = 69
-------------+---------------------------------- F(7, 61) = 4.88
Model | 839.550121 7 119.935732 Prob > F = 0.0002
Residual | 1500.65278 61 24.6008652 R-squared = 0.3588
-------------+---------------------------------- Adj R-squared = 0.2852
Total | 2340.2029 68 34.4147485 Root MSE = 4.9599
-------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
foreign#rep78 |
Domestic#2 | -1.875 3.921166 -0.48 0.634 -9.715855 5.965855
Domestic#3 | -2 3.634773 -0.55 0.584 -9.268178 5.268178
Domestic#4 | -2.555556 3.877352 -0.66 0.512 -10.3088 5.19769
Domestic#5 | 11 4.959926 2.22 0.030 1.082015 20.91798
Foreign#1 | 0 (empty)
Foreign#2 | 0 (empty)
Foreign#3 | 2.333333 4.527772 0.52 0.608 -6.720507 11.38717
Foreign#4 | 3.888889 3.877352 1.00 0.320 -3.864357 11.64213
Foreign#5 | 5.333333 3.877352 1.38 0.174 -2.419912 13.08658
|
_cons | 21 3.507197 5.99 0.000 13.98693 28.01307
-------------------------------------------------------------------------------
为了重现前面R的Stata内容，我们可以重新编码这两个变量foreign和rep78：
. reg mpg i.foreign2#i.rep2
note: 0b.foreign2#1.rep2 identifies no observations in the sample
note: 0b.foreign2#2.rep2 identifies no observations in the sample
Source | SS df MS Number of obs = 69
-------------+---------------------------------- F(7, 61) = 4.88
Model | 839.550121 7 119.935732 Prob > F = 0.0002
Residual | 1500.65278 61 24.6008652 R-squared = 0.3588
-------------+---------------------------------- Adj R-squared = 0.2852
Total | 2340.2029 68 34.4147485 Root MSE = 4.9599
-------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
foreign2#rep2 |
0 1 | 0 (empty)
0 2 | 0 (empty)
0 3 | -3 3.306617 -0.91 0.368 -9.61199 3.61199
0 4 | -1.444444 2.338132 -0.62 0.539 -6.119827 3.230938
1 0 | 5.666667 3.877352 1.46 0.149 -2.086579 13.41991
1 1 | -5.333333 3.877352 -1.38 0.174 -13.08658 2.419912
1 2 | -7.208333 2.410091 -2.99 0.004 -12.02761 -2.389059
1 3 | -7.333333 1.909076 -3.84 0.000 -11.15077 -3.515899
1 4 | -7.888889 2.338132 -3.37 0.001 -12.56427 -3.213506
|
_cons | 26.33333 1.653309 15.93 0.000 23.02734 29.63933
-------------------------------------------------------------------------------
相同的方法适用于在 中重现Stata结果R，只需重新定义levels这两个因子变量。
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