Ralph M Ralph M - 1 month ago 11
R Question

How to conduct linear hypothesis test on regression coefficients with a clustered covariance matrix?

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'))


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
.

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


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


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

Thanks!

Answer

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|)")))
  }

Let's have a test:

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

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 ***

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

Remark

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]

rather than just the sum

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