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Whether analyzing a block-randomized experiment or adding fixed effects for a panel model, absorbing group means can speed up estimation time. The fixed_effects argument in both lm_robust and iv_robust allows you to do just that, although the speed gains are greatest with “HC1” standard errors. Specifying fixed effects is really simple.

library(estimatr)
lmr_out <- lm_robust(mpg ~ hp, data = mtcars, fixed_effects = ~ cyl)
lmr_out
##       Estimate Std. Error   t value  Pr(>|t|)    CI Lower    CI Upper DF
## hp -0.02403883 0.01503818 -1.598521 0.1211523 -0.05484314 0.006765475 28
lmr_out$fixed_effects
##     cyl4     cyl6     cyl8 
## 28.65012 22.68246 20.12927

Before proceeding, three quick notes:

  • Most of the speed gains occur when estimating “HC1” robust standard errors, or “stata” standard errors when there is clustering. This is because most of the speed gains come from avoiding inverting a large matrix of group dummies, but this step is still necessary for “HC2”, “HC3”, and “CR2” standard errors.
  • While you can specify multiple sets of fixed effects, such as fixed_effects = ~ year + country, please ensure that your model is well-specified if you do so. If there are dependencies or overlapping groups across multiple sets of fixed effects, we cannot guarantee the correct degrees of freedom.
  • For now, weighted “CR2” estimation is not possible with fixed_effects.

Speed gains

In general, our speed gains will be greatest as the number of groups/fixed effects is large relative to the number of observations. Imagine we have 300 matched-pairs in an experiment.

# Load packages for comparison
library(microbenchmark)
library(sandwich)
library(lmtest)

# Create matched-pairs dataset using fabricatr
set.seed(40)
library(fabricatr)
dat <- fabricate(
  blocks = add_level(N = 300),
  indiv = add_level(N = 2, z = sample(0:1), y = rnorm(N) + z)
)
head(dat)
##   blocks indiv z          y
## 1    001   001 1  1.4961828
## 2    001   002 0 -0.8595843
## 3    002   003 1  0.1709400
## 4    002   004 0 -0.3215731
## 5    003   005 1 -0.3037704
## 6    003   006 0 -1.4214866
# With HC2
microbenchmark(
  `base + sandwich` = {
    lo <- lm(y ~ z + factor(blocks), dat)
    coeftest(lo, vcov = vcovHC(lo, type = "HC2"))
  },
  `lm_robust` = lm_robust(y ~ z + factor(blocks), dat),
  `lm_robust + fes` = lm_robust(y ~ z, data = dat, fixed_effects = ~ blocks),
  times = 50
)
## Unit: milliseconds
##             expr       min        lq     mean    median       uq       max
##  base + sandwich 261.03530 343.18088 446.2037 395.15294 539.9669  799.1960
##        lm_robust  81.58876 116.21489 210.0907 142.38783 282.8995 1054.2574
##  lm_robust + fes  51.06416  78.48118 117.6341  89.17866 141.1214  406.9015
##  neval cld
##     50 a  
##     50  b 
##     50   c

Speed gains are considerably greater with HC1 standard errors. This is because we need to get the hat matrix for HC2, HC3, and CR2 standard errors, which requires inverting that large matrix of dummies we previously avoided doing. HC0, HC1, CR0, and CRstata standard errors do not require this inversion.

# With HC1
microbenchmark(
  `base + sandwich` = {
    lo <- lm(y ~ z + factor(blocks), dat)
    coeftest(lo, vcov = vcovHC(lo, type = "HC1"))
  },
  `lm_robust` = lm_robust(
    y ~ z + factor(blocks),
    dat,
    se_type = "HC1"
  ),
  `lm_robust + fes` = lm_robust(
    y ~ z, 
    data = dat,
    fixed_effects = ~ blocks,
    se_type = "HC1"
  ),
  times = 50
)
## Unit: milliseconds
##             expr       min        lq     mean    median        uq       max
##  base + sandwich 247.42021 291.57124 424.4590 376.14638 501.08711 1194.5689
##        lm_robust  72.96049  98.64266 131.1418 119.12162 155.77420  282.9733
##  lm_robust + fes   7.94056  13.04199  26.4304  16.08091  22.24237  103.8111
##  neval cld
##     50 a  
##     50  b 
##     50   c