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 28lmr_out$fixed_effects## cyl4 cyl6 cyl8
## 28.65012 22.68246 20.12927Before 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
## base + sandwich 187.96590 195.35559 208.74518 199.32343 209.55099
## lm_robust 79.70901 82.08865 87.66793 84.16803 86.63896
## lm_robust + fes 44.77912 46.04134 53.91802 47.87909 50.24418
## max neval
## 332.6788 50
## 158.8674 50
## 166.5931 50Speed 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
## base + sandwich 193.774441 199.27979 207.23697 203.35366 207.67662
## lm_robust 68.119831 71.04221 73.57887 72.74155 74.83757
## lm_robust + fes 9.729048 10.10144 12.55408 10.30069 10.67900
## max neval
## 283.43759 50
## 98.15688 50
## 72.78832 50