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 221.28409 225.66227 231.34252 227.07283 231.05973
## lm_robust 82.63381 83.68475 87.63824 85.85196 88.59431
## lm_robust + fes 47.61995 48.47950 51.45073 48.77673 51.01346
## max neval
## 301.5375 50
## 154.0477 50
## 134.7939 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 221.354691 225.873497 230.442076 226.764015 229.680757
## lm_robust 68.798423 69.975511 71.264803 70.489942 71.710894
## lm_robust + fes 7.250985 7.874341 8.551306 8.087355 8.333747
## max neval
## 304.19881 50
## 75.78107 50
## 13.80425 50