如何使用聚类协方差矩阵对回归系数进行线性假设检验? [英] How to conduct linear hypothesis test on regression coefficients with a clustered covariance matrix?

问题描述

我对在R中进行线性回归后计算系数的线性组合的估计值和标准误差感兴趣.例如，假设我有回归并检验:

I am interested in calculating estimates and standard errors for linear combinations of coefficients after a linear regression in R. For example, suppose I have the regression and test:

data(mtcars)
library(multcomp)
lm1 <- lm(mpg ~ cyl + hp, data = mtcars)
summary(glht(lm1, linfct = 'cyl + hp = 0'))

这将估计cyl和hp上的系数之和的值，并基于lm产生的协方差矩阵提供标准误差.

This will estimate the value of the sum of the coefficients on cyl and hp, and provide the standard error based on the covariance matrix produced by lm.

但是，假设我想将我的标准错误集中在第三个变量上:

But, suppose I want to cluster my standard errors, on a third variable:

data(mtcars)
library(multcomp)
library(lmtest)
library(multiwayvcov)
lm1 <- lm(mpg ~ cyl + hp, data = mtcars)
vcv <- cluster.vcov(lm1, cluster = mtcars$am)
ct1 <- coeftest(lm1,vcov. = vcv)

ct1包含我通过am进行聚类的SE.但是，如果我尝试在glht中使用ct1对象，则会显示一条错误消息

ct1 contains the SEs for my clustering by am. However, if I try to use the ct1 object in glht, you get an error saying

modelparm.default(model，...)中的错误: 找不到模型"的"coef"方法！

Error in modelparm.default(model, ...) : no ‘coef’ method for ‘model’ found!

关于如何使用聚类方差协方差矩阵进行线性假设的任何建议?

Any advice on how to do the linear hypothesis with the clustered variance covariance matrix?

谢谢！

推荐答案

glht(ct1, linfct = 'cyl + hp = 0')将不起作用，因为ct1不是glht对象，并且不能通过as.glht强制这样做.我不知道是否有一个软件包或一个现有的函数来执行此操作，但是要自己完成这项工作并不困难.下面的小功能可以做到这一点:

glht(ct1, linfct = 'cyl + hp = 0') won't work, because ct1 is not a glht object and can not be coerced to such via as.glht. I don't know whether there is a package or an existing function to do this, but this is not a difficult job to work out ourselves. The following small function does it:

LinearCombTest <- function (lmObject, vars, .vcov = NULL) {
  ## if `.vcov` missing, use the one returned by `lm`
  if (is.null(.vcov)) .vcov <- vcov(lmObject)
  ## estimated coefficients
  beta <- coef(lmObject)
  ## sum of `vars`
  sumvars <- sum(beta[vars])
  ## get standard errors for sum of `vars`
  se <- sum(.vcov[vars, vars]) ^ 0.5
  ## perform t-test on `sumvars`
  tscore <- sumvars / se
  pvalue <- 2 * pt(abs(tscore), lmObject$df.residual, lower.tail = FALSE)
  ## return a matrix
  matrix(c(sumvars, se, tscore, pvalue), nrow = 1L,
         dimnames = list(paste0(paste0(vars, collapse = " + "), " = 0"),
                         c("Estimate", "Std. Error", "t value", "Pr(>|t|)")))
  }

让我们进行测试:

data(mtcars)
lm1 <- lm(mpg ~ cyl + hp, data = mtcars)
library(multiwayvcov)
vcv <- cluster.vcov(lm1, cluster = mtcars$am)

如果在LinearCombTest中未指定.vcov，则与multcomp::glht相同:

If we leave .vcov unspecified in LinearCombTest, it is as same as multcomp::glht:

LinearCombTest(lm1, c("cyl","hp"))

#              Estimate Std. Error   t value     Pr(>|t|)
#cyl + hp = 0 -2.283815  0.5634632 -4.053175 0.0003462092

library(multcomp)
summary(glht(lm1, linfct = 'cyl + hp = 0'))

#Linear Hypotheses:
#              Estimate Std. Error t value Pr(>|t|)    
#cyl + hp == 0  -2.2838     0.5635  -4.053 0.000346 ***

如果我们提供协方差，它将满足您的要求:

If we provide a covariance, it does what you want:

LinearCombTest(lm1, c("cyl","hp"), vcv)

#              Estimate Std. Error  t value    Pr(>|t|)
#cyl + hp = 0 -2.283815  0.7594086 -3.00736 0.005399071

---

备注

LinearCombTest在

LinearCombTest is upgraded at Get p-value for group mean difference without refitting linear model with a new reference level, where we can test any combination with combination coefficients alpha:

alpha[1] * vars[1] + alpha[2] * vars[2] + ... + alpha[k] * vars[k]

不仅仅是总和

vars[1] + vars[2] + ... + vars[k]

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