如何解决修正 lm 函数中的稳健/聚类标准错误或替换结果
在 CrossValidated 上交叉发布。
不久前,我问了 this question,这是关于在使用 IV/2SLS 时纠正标准错误,并且第一阶段有一个 tobit 分布,我从 jay.sf 得到了一个惊人的答案(示例数据在底部)。他为我提供了以下功能:
vcov2sls <- function(s1,s2,data,type=2) {
## get y names
y1.nm <- gsub(".*=\\s(.*)(?=\\s~).*","\\1",deparse(s1$call)[1],perl=TRUE)
y2.nm <- as.character(s2$terms)[2]
## auxilliary model matrix
X <- cbind(`(Intercept)`=1,data[,y1.nm,F],model.matrix(s2)[,-(1:2)])
## get y
y <- data[,y2.nm]
## betas second stage
b <- s2$coefficients
## calculate corrected sums of squares
sse <- sum((y - b %*% t(X))^2)
rmse <- sqrt(mean(s2$residuals^2)) ## RMSE 2nd stage
V0 <- vcov(s2) ## biased vcov 2nd stage
dof <- s2$df.residual ## degrees of freedom 2nd stage
## calculate corrected RMSE
rmse.c <- sqrt(sse/dof)
## calculate corrected vcov
V <- (rmse.c/rmse)^2 * V0
return(V)
}
所以我正在寻找的是一个函数,我可以在其中提供 vcov 矩阵(vcov2sls
),并且具有稳健的聚类标准误差。然而,它们似乎都属于相同的 vcov 矩阵选项。因此,如果我提供一个,我已经必须确保 se 是集群和健壮的。所以我想我本质上是在问如何使 vcov2sls
函数具有健壮和集群错误。显然,任何其他导致相同实际结果的解决方案也会很棒。
但是我想使用jay.sf的函数,当第一阶段是lm
时,聚类参与汇总(source),例如:
first_stage_ols <- lm(y~x,data=DT)
summary(first_stage_ols,robust=T)
有没有办法从 lm 函数中纠正标准错误,或者(在结果中替换它们),或者调整 vcov2sls
函数以考虑稳健/聚类标准错误?
编辑:我知道 lmtest:coeftest
也存在,但我希望能够使用 weights
。见this link。我无法确定这在 lmtest:coeftest
中是否可行。
编辑 I - 尝试测试人员解决方案
所以我尝试了测试人员在两种情况下的回答。首先,我从一个 tobit 移动到一个 lm,反之亦然。
# Tobit -> LM
library(lmtest)
library(sandwich)
## run with lm ##
s1.tobit <- AER::tobit(taxrate ~ votewon + industry + size + urbanisation + vote,data=DF)
# cluster and adjust ses
s1.robust <- vcovCL(s1.tobit,cluster = ~ industry)
s1.robust.se <- sqrt(diag(s1.robust))
s1.summary <- summary(s1.tobit)
s1.summary$coefficients[,2] <- s1.robust.se
yhat <- fitted(s1.tobit)
s2.lm <- lm(sales ~ yhat + industry + size + urbanisation + vote,data=DF)
lmtest::coeftest(s2.lm,vcov.=vcov2sls(s1.summary,s2.lm,DF))
# WORKS!
反之亦然:
# LM -> tobit
library(lmtest)
library(sandwich)
## run with lm ##
s1.lm <- lm(taxrate ~ votewon + industry + size + urbanisation + vote,data=DF)
# cluster and adjust ses
s1.robust <- vcovCL(s1.lm,cluster = ~ industry)
s1.robust.se <- sqrt(diag(s1.robust))
s1.summary <- summary(s1.lm)
s1.summary$coefficients[,2] <- s1.robust.se
yhat <- fitted(s1.lm)
s2.tobit <- AER::tobit(sales ~ yhat + industry + size + urbanisation + vote,data=DF)
and then ????
# DOES NOT WORK,NO WAY TO ADD THE VCOV TO TOBIT
编辑结束
EDIT II - 测试 lm_robust 和 manual 之间的 p 值
当使用 lm_robust
时,第一阶段的结果如下:
Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF
(Intercept) 25.3890287 2.1726518 11.6857327 0.009184928 15.393996 35.3840612 1.870781
votewon -0.9900966 2.1099738 -0.4692459 0.687605609 -10.636404 8.6562105 1.882014
industryE -0.7564888 0.3710393 -2.0388372 0.184868777 -2.434709 0.9217314 1.901678
industryF -2.6639323 0.3058024 -8.7112866 0.013649538 -4.002800 -1.3250647 1.964416
size -0.5291956 0.5523497 -0.9580807 0.443894805 -3.036862 1.9784705 1.894753
urbanisationB -1.5851495 2.2454251 -0.7059463 0.554845739 -11.464414 8.2941148 1.954657
urbanisationC -2.7234541 0.3573827 -7.6205532 0.020124544 -4.365749 -1.0811587 1.872744
vote 3.1749142 2.4600297 1.2906000 0.341874112 -9.076839 15.4266675 1.740353
但是,在进行手动计算时,p 值非常不同:
s1.summary
Call:
lm(formula = taxrate ~ votewon + industry + size + urbanisation +
vote,data = DF)
Residuals:
Min 1Q Median 3Q Max
-11.2747 -4.3212 -0.6788 4.3677 10.7369
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.3890 2.1506 13.845 <2e-16 ***
votewon -0.9901 2.1742 -0.676 0.5007
industryE -0.7565 0.3492 -0.557 0.5792
industryF -2.6639 0.2877 -1.855 0.0668 .
size -0.5292 0.5109 -1.250 0.2145
urbanisationB -1.5851 2.2311 -1.098 0.2753
urbanisationC -2.7235 0.3474 -1.704 0.0918 .
vote 3.1749 2.4840 2.105 0.0380 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.623 on 92 degrees of freedom
Multiple R-squared: 0.1054,Adjusted R-squared: 0.03734
F-statistic: 1.549 on 7 and 92 DF,p-value: 0.1609
这只是第一阶段。
示例数据
DF <- structure(list(country = c("C","C","J","B","F","E","D","I","H","G","A","F"),year = c(2005,2010,2005,2005),sales = c(15.48,12.39,3.72,23.61,4,31.87,25.33,7.64,-0.26,2.9,15.48,2.9),industry = c("D",urbanisation = c("B","B"),size = c(1,1,5,2,3,5),base_rate = c(14L,14L,19L,30L,20L,29L,24L,17L,33L,23L,20L),taxrate = c(12L,12L,21L,18L,32L,22L,25L,vote = c(0,1),votewon = c(0,1)),class = "data.frame",row.names = c(NA,-100L))
## convert variables to factors beforehand
DF[c(1,6,9,10)] <- lapply(DF[c(1,10)],factor)
s1.tobit <- AER::tobit(taxrate ~ votewon + industry + size + urbanisation + vote,left=12,right=33,data=DF)
yhat <- fitted(s1.tobit)
s2.tobit <- lm(sales ~ yhat + industry + size + urbanisation + vote,data=DF)
lmtest::coeftest(s2.tobit,vcov.=vcov2sls(s1.tobit,s2.tobit,DF))
解决方法
编辑:
通过这种方式,您可以在第一阶段运行 lm,调整模型的 SE 并使用它来覆盖 summary(lm)
生成的 SE。然后,您可以估计第二阶段并使用带有 coeftest()
的自定义函数。不确定聚类,但这应该大致有效,不是吗?
library(lmtest)
library(sandwich)
## run with lm ##
s1.lm <- lm(taxrate ~ votewon + industry + size + urbanisation + vote,data=DF)
# cluster and adjust ses
s1.robust <- vcovCL(s1.lm,cluster = ~ industry)
s1.robust.se <- sqrt(diag(s1.robust))
s1.summary <- summary(s1.lm)
s1.summary$coefficients[,2] <- s1.robust.se
yhat <- fitted(s1.lm)
s2.lm <- lm(sales ~ yhat + industry + size + urbanisation + vote,data=DF)
lmtest::coeftest(s2.lm,vcov.=vcov2sls(s1.summary,s2.lm,DF))
查看 estimatr
包,尤其是 lm_robust
。我不是 100% 确定您打算做什么,但是您可以通过运行以下命令获得可靠的标准错误:
library(estimatr)
lm1 <-
lm_robust(
mpg ~ hp,data = mtcars,clusters = cyl,weights = wt,se_type = "stata" # alternatives: CR0,CR1
)
summary(lm1)
使用上面的示例,这大致是您要查找的内容吗?请注意,lm_robust 已经调整了 SE。
s1.lm <- lm_robust(taxrate ~ votewon + industry + size + urbanisation + vote,data = DF)
yhat <- fitted(s1.lm)
s2.lm <- lm(sales ~ yhat + industry + size + urbanisation + vote,data = DF)
> lmtest::coeftest(s2.lm,vcov. = vcov2sls(s1.lm,DF))
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -18.45116 62.14257 -0.2969 0.7672
yhat 1.57784 2.72176 0.5797 0.5636
industryE 0.98174 5.10677 0.1922 0.8480
industryF 2.09036 7.25181 0.2883 0.7738
size2 -8.85327 12.43454 -0.7120 0.4783
size3 -5.74011 7.14973 -0.8028 0.4242
size4 -10.79326 13.14534 -0.8211 0.4138
size5 -3.38280 5.45691 -0.6199 0.5369
urbanisationB -1.74588 6.34107 -0.2753 0.7837
urbanisationC -2.00370 6.48533 -0.3090 0.7581
vote1 -1.01661 6.49424 -0.1565 0.8760
> lmtest::coeftest(s2.lm)
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -18.45116 46.39576 -0.3977 0.6918
yhat 1.57784 2.03207 0.7765 0.4395
industryE 0.98174 3.81273 0.2575 0.7974
industryF 2.09036 5.41421 0.3861 0.7004
size2 -8.85327 9.28365 -0.9536 0.3428
size3 -5.74011 5.33801 -1.0753 0.2851
size4 -10.79326 9.81434 -1.0997 0.2744
size5 -3.38280 4.07414 -0.8303 0.4086
urbanisationB -1.74588 4.73425 -0.3688 0.7132
urbanisationC -2.00370 4.84196 -0.4138 0.6800
vote1 -1.01661 4.84861 -0.2097 0.8344
我会根据您的评论更新我的答案。
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