异方差回归校正标准误差

发布于 2024-10-06 13:35:57 字数 378 浏览 4 评论 0原文

我想找到与 Stata 输出最相似的 R 实现，用于拟合具有异方差校正标准误差的最小二乘回归函数。

具体来说，我希望修正后的标准误差位于“摘要”中，而不必为我的第一轮假设检验进行额外的计算。我正在寻找一个像 Eviews 和 Stata 提供的那样“干净”的解决方案。

到目前为止，使用“lmtest”包，我能想到的最好的办法是：

model <- lm(...)
coeftest(model, vcov = hccm)

这给了我我想要的输出，但它似乎没有使用“coeftest”来达到其既定目的。我还必须使用带有不正确标准错误的摘要来读取 R^2 和 F 统计数据等。考虑到 R 的动态性，我认为应该存在一个“一行”解决方案来解决这个问题。

原文

I would like to find the R implementation that most closely resembles Stata output for fitting a least squares regression function with Heteroskedastic Corrected Standard Errors.

Specifically, I would like the corrected standard errors to be in the "summary" and not have to do additional calculations for my initial round of hypothesis testing. I am looking for a solution that is as "clean" as what Eviews and Stata provide.

So far, using the "lmtest" package, the best I can come up with is:

model <- lm(...)
coeftest(model, vcov = hccm)

This gives me the output that I want, but it does not seem to be using "coeftest" for its stated purpose. I would also have to use the summary with the incorrect standard errors to read off the R^2 and F stat, etc. I feel that there should exist a "one line" solution to this problem given how dynamic R is.

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铜锣湾横着走 2024-10-13 13:35:57

我认为您在 lmtest 包中的 coeftest 上走在正确的轨道上。看一下 sandwich 包，它包含此功能，并且旨在与您已经找到的 lmtest 包协同工作。

> # generate linear regression relationship
> # with Homoskedastic variances
> x <- sin(1:100)
> y <- 1 + x + rnorm(100)
> ## model fit and HC3 covariance
> fm <- lm(y ~ x)
> vcovHC(fm)
            (Intercept)           x
(Intercept) 0.010809366 0.001209603
x           0.001209603 0.018353076
> coeftest(fm, vcov. = vcovHC)

t test of coefficients:

            Estimate Std. Error t value  Pr(>|t|)    
(Intercept)  1.01973    0.10397  9.8081 3.159e-16 ***
x            0.93992    0.13547  6.9381 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

要获得 F 测试，请查看函数 waldtest()：

> waldtest(fm, vcov = vcovHC)
Wald test

Model 1: y ~ x
Model 2: y ~ 1
  Res.Df Df      F    Pr(>F)    
1     98                        
2     99 -1 48.137 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

如果您想要单行代码，您总是可以编写一个简单的函数来将这两个函数组合起来...

中有很多示例使用 HC 和 HAC 协方差矩阵估计器进行计量经济学计算小插图附带了连接 lmtest 和三明治的三明治包，可以做你想做的事情。

编辑：一行可以很简单：

mySummary <- function(model, VCOV) {
    print(coeftest(model, vcov. = VCOV))
    print(waldtest(model, vcov = VCOV))
}

我们可以这样使用（在上面的示例中）：

> mySummary(fm, vcovHC)

t test of coefficients:

            Estimate Std. Error t value  Pr(>|t|)    
(Intercept)  1.01973    0.10397  9.8081 3.159e-16 ***
x            0.93992    0.13547  6.9381 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Wald test

Model 1: y ~ x
Model 2: y ~ 1
  Res.Df Df      F    Pr(>F)    
1     98                        
2     99 -1 48.137 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

I think you are on the right track with coeftest in package lmtest. Take a look at the sandwich package which includes this functionality and is designed to work hand in hand with the lmtest package you have already found.

> # generate linear regression relationship
> # with Homoskedastic variances
> x <- sin(1:100)
> y <- 1 + x + rnorm(100)
> ## model fit and HC3 covariance
> fm <- lm(y ~ x)
> vcovHC(fm)
            (Intercept)           x
(Intercept) 0.010809366 0.001209603
x           0.001209603 0.018353076
> coeftest(fm, vcov. = vcovHC)

t test of coefficients:

            Estimate Std. Error t value  Pr(>|t|)    
(Intercept)  1.01973    0.10397  9.8081 3.159e-16 ***
x            0.93992    0.13547  6.9381 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

To get the F test, look at function waldtest():

> waldtest(fm, vcov = vcovHC)
Wald test

Model 1: y ~ x
Model 2: y ~ 1
  Res.Df Df      F    Pr(>F)    
1     98                        
2     99 -1 48.137 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

You could always cook up a simple function to combine these two for you if you wanted the one-liner...

There are lots of examples in the Econometric Computing with HC and HAC Covariance Matrix Estimators vignette that comes with the sandwich package of linking lmtest and sandwich to do what you want.

Edit: A one-liner could be as simple as:

mySummary <- function(model, VCOV) {
    print(coeftest(model, vcov. = VCOV))
    print(waldtest(model, vcov = VCOV))
}

Which we can use like this (on the examples from above):

> mySummary(fm, vcovHC)

t test of coefficients:

            Estimate Std. Error t value  Pr(>|t|)    
(Intercept)  1.01973    0.10397  9.8081 3.159e-16 ***
x            0.93992    0.13547  6.9381 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Wald test

Model 1: y ~ x
Model 2: y ~ 1
  Res.Df Df      F    Pr(>F)    
1     98                        
2     99 -1 48.137 4.313e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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陌生 2024-10-13 13:35:57

我找到了一个 R 函数，它完全可以满足您的需求。它为您提供可靠的标准误差，而无需进行额外的计算。您在 lm.object 上运行 summary()，如果您设置参数 robust=T，它会返回类似于 Stata 的异方差一致标准错误。

summary(lm.object, robust=T)

您可以在 https://economictheoryblog.com/ 上找到该函数2016/08/08/robust-standard-errors-in-r/

I found an R function that does exactly what you are looking for. It gives you robust standard errors without having to do additional calculations. You run summary() on an lm.object and if you set the parameter robust=T it gives you back Stata-like heteroscedasticity consistent standard errors.

summary(lm.object, robust=T)

You can find the function on https://economictheoryblog.com/2016/08/08/robust-standard-errors-in-r/

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a√萤火虫的光℡ 2024-10-13 13:35:57

现在有一个使用 estimatr 中的 lm_robust 的单行解决方案package，您可以从 CRAN install.packages(estimatr) 安装它。

> library(estimatr)
> lmro <- lm_robust(mpg ~ hp, data = mtcars, se_type = "stata")
> summary(lmro)

Call:
lm_robust(formula = mpg ~ hp, data = mtcars, se_type = "stata")

Standard error type:  HC1 

Coefficients:
            Estimate Std. Error  Pr(>|t|) CI Lower CI Upper DF
(Intercept) 30.09886    2.07661 4.348e-15 25.85785 34.33987 30
hp          -0.06823    0.01356 2.132e-05 -0.09592 -0.04053 30

Multiple R-squared:  0.6024 ,   Adjusted R-squared:  0.5892 
F-statistic: 45.46 on 1 and 30 DF,  p-value: 1.788e-07

您还可以获得整洁的输出：

> tidy(lmro)
         term    estimate std.error      p.value    ci.lower
1 (Intercept) 30.09886054 2.0766149 4.347723e-15 25.85784704
2          hp -0.06822828 0.0135604 2.131785e-05 -0.09592231
     ci.upper df outcome
1 34.33987404 30     mpg
2 -0.04053425 30     mpg

“stata”标准错误默认为“HC1”标准错误，这是Stata中默认的rob标准错误。您还可以获得“classical”、“HC0”、“HC1”、“HC2”、“HC3” 以及各种集群标准错误（包括与 Stata 匹配的错误）。

There is now a one-line solution using lm_robust from the estimatr package, which you can install from CRAN install.packages(estimatr).

> library(estimatr)
> lmro <- lm_robust(mpg ~ hp, data = mtcars, se_type = "stata")
> summary(lmro)

Call:
lm_robust(formula = mpg ~ hp, data = mtcars, se_type = "stata")

Standard error type:  HC1 

Coefficients:
            Estimate Std. Error  Pr(>|t|) CI Lower CI Upper DF
(Intercept) 30.09886    2.07661 4.348e-15 25.85785 34.33987 30
hp          -0.06823    0.01356 2.132e-05 -0.09592 -0.04053 30

Multiple R-squared:  0.6024 ,   Adjusted R-squared:  0.5892 
F-statistic: 45.46 on 1 and 30 DF,  p-value: 1.788e-07

You can also get tidy output:

> tidy(lmro)
         term    estimate std.error      p.value    ci.lower
1 (Intercept) 30.09886054 2.0766149 4.347723e-15 25.85784704
2          hp -0.06822828 0.0135604 2.131785e-05 -0.09592231
     ci.upper df outcome
1 34.33987404 30     mpg
2 -0.04053425 30     mpg

The "stata" standard errors default to "HC1" standard errors, which are the default rob standard errors in Stata. You can also get "classical", "HC0", "HC1", "HC2", "HC3" and various clustered standard errors as well (including those that match Stata).

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