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

covariance, linear-regression, lm, r, regression

Solution

`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]

Problem

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!

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