This function is a wrapper for lm_robust
that
is useful for estimating treatment effects with pre-treatment covariate
data. This implements the method described by Lin (2013).
lm_lin(
formula,
covariates,
data,
weights,
subset,
clusters,
se_type = NULL,
ci = TRUE,
alpha = 0.05,
return_vcov = TRUE,
try_cholesky = FALSE
)
an object of class formula, as in lm
, such as
Y ~ Z
with only one variable on the right-hand side, the treatment
a right-sided formula with pre-treatment covariates on
the right hand side, such as ~ x1 + x2 + x3
.
A data.frame
the bare (unquoted) names of the weights variable in the supplied data.
An optional bare (unquoted) expression specifying a subset of observations to be used.
An optional bare (unquoted) name of the variable that corresponds to the clusters in the data.
The sort of standard error sought. If clusters
is
not specified the options are "HC0", "HC1" (or "stata", the equivalent),
"HC2" (default), "HC3", or "classical". If clusters
is specified the
options are "CR0", "CR2" (default), or "stata" are
permissible.
logical. Whether to compute and return p-values and confidence intervals, TRUE by default.
The significance level, 0.05 by default.
logical. Whether to return the variance-covariance matrix for later usage, TRUE by default.
logical. Whether to try using a Cholesky decomposition to solve least squares instead of a QR decomposition, FALSE by default. Using a Cholesky decomposition may result in speed gains, but should only be used if users are sure their model is full-rank (i.e., there is no perfect multi-collinearity)
An object of class "lm_robust"
.
The post-estimation commands functions summary
and tidy
return results in a data.frame
. To get useful data out of the return,
you can use these data frames, you can use the resulting list directly, or
you can use the generic accessor functions coef
, vcov
,
confint
, and predict
. Marginal effects and uncertainty about
them can be gotten by passing this object to
margins
from the margins.
Users who want to print the results in TeX of HTML can use the
extract
function and the texreg package.
An object of class "lm_robust"
is a list containing at least the
following components:
the estimated coefficients
the estimated standard errors
the t-statistic
the estimated degrees of freedom
the p-values from a two-sided t-test using coefficients
, std.error
, and df
the lower bound of the 1 - alpha
percent confidence interval
the upper bound of the 1 - alpha
percent confidence interval
a character vector of coefficient names
the significance level specified by the user
the standard error type specified by the user
the residual variance
the number of observations used
the number of columns in the design matrix (includes linearly dependent columns!)
the rank of the fitted model
the fitted variance covariance matrix
The \(R^2\), $$R^2 = 1 - Sum(e[i]^2) / Sum((y[i] - y^*)^2),$$ where \(y^*\) is the mean of \(y[i]\) if there is an intercept and zero otherwise, and \(e[i]\) is the ith residual.
The \(R^2\) but penalized for having more parameters, rank
whether or not weights were applied
the original function call
the matrix of predicted means
We also return terms
and contrasts
, used by predict
,
and scaled_center
the means of each of the covariates used for centering them
This function is simply a wrapper for lm_robust
and implements
the Lin estimator (see the reference below). This method
pre-processes the data by taking the covariates specified in the
`covariates`
argument, centering them by subtracting from each covariate
its mean, and interacting them with the treatment. If the treatment has
multiple values, a series of dummies for each value is created and each of
those is interacted with the demeaned covariates. More details can be found
in the
Getting Started vignette
and the
mathematical notes.
#' @references Freedman, David A. 2008. "On Regression Adjustments in Experiments with Several Treatments." The Annals of Applied Statistics. JSTOR, 176-96. doi: 10.1214/07-AOAS143 .
Lin, Winston. 2013. "Agnostic Notes on Regression Adjustments to Experimental Data: Reexamining Freedman's Critique." The Annals of Applied Statistics 7 (1). Institute of Mathematical Statistics: 295-318. doi: 10.1214/12-AOAS583 .
library(fabricatr)
library(randomizr)
dat <- fabricate(
N = 40,
x = rnorm(N, mean = 2.3),
x2 = rpois(N, lambda = 2),
x3 = runif(N),
y0 = rnorm(N) + x,
y1 = rnorm(N) + x + 0.35
)
dat$z <- complete_ra(N = nrow(dat))
dat$y <- ifelse(dat$z == 1, dat$y1, dat$y0)
# Same specification as lm_robust() with one additional argument
lmlin_out <- lm_lin(y ~ z, covariates = ~ x, data = dat)
tidy(lmlin_out)
#> term estimate std.error statistic p.value conf.low conf.high
#> 1 (Intercept) 2.0074002 0.2012088 9.9767032 6.611620e-12 1.5993299 2.4154705
#> 2 z 0.7263528 0.3037565 2.3912337 2.214176e-02 0.1103061 1.3423996
#> 3 x_c 1.0673003 0.2721532 3.9216889 3.786550e-04 0.5153480 1.6192527
#> 4 z:x_c -0.2815330 0.3235071 -0.8702529 3.899283e-01 -0.9376358 0.3745698
#> df outcome
#> 1 36 y
#> 2 36 y
#> 3 36 y
#> 4 36 y
# Works with multiple pre-treatment covariates
lm_lin(y ~ z, covariates = ~ x + x2, data = dat)
#> Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper
#> (Intercept) 2.0331904 0.2035346 9.9894110 1.198631e-11 1.61955838 2.4468224
#> z 0.6874490 0.3118326 2.2045450 3.435353e-02 0.05372891 1.3211692
#> x_c 1.1154732 0.2539604 4.3923109 1.038122e-04 0.59936348 1.6315829
#> x2_c 0.2456971 0.2805576 0.8757456 3.873136e-01 -0.32446459 0.8158588
#> z:x_c -0.3294245 0.3067964 -1.0737561 2.904938e-01 -0.95290983 0.2940608
#> z:x2_c -0.1146326 0.3618812 -0.3167687 7.533560e-01 -0.85006364 0.6207984
#> DF
#> (Intercept) 34
#> z 34
#> x_c 34
#> x2_c 34
#> z:x_c 34
#> z:x2_c 34
# Also centers data AFTER evaluating any functions in formula
lmlin_out2 <- lm_lin(y ~ z, covariates = ~ x + log(x3), data = dat)
lmlin_out2$scaled_center["log(x3)"]
#> log(x3)
#> -0.7815509
mean(log(dat$x3))
#> [1] -0.7815509
# Works easily with clusters
dat$clusterID <- rep(1:20, each = 2)
dat$z_clust <- cluster_ra(clusters = dat$clusterID)
lm_lin(y ~ z_clust, covariates = ~ x, data = dat, clusters = clusterID)
#> Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper
#> (Intercept) 2.1869918 0.2599259 8.4139039 6.338923e-05 1.573233032 2.8007505
#> z_clust 0.1547201 0.3441864 0.4495242 6.598847e-01 -0.582978576 0.8924188
#> x_c 0.6678927 0.2632028 2.5375595 5.052778e-02 -0.002227515 1.3380129
#> z_clust:x_c 0.5497024 0.3559260 1.5444288 1.576286e-01 -0.258197236 1.3576021
#> DF
#> (Intercept) 7.049192
#> z_clust 14.103467
#> x_c 5.165385
#> z_clust:x_c 8.804119
# Works with multi-valued treatments
dat$z_multi <- sample(1:3, size = nrow(dat), replace = TRUE)
lm_lin(y ~ z_multi, covariates = ~ x, data = dat)
#> Estimate Std. Error t value Pr(>|t|) CI Lower
#> (Intercept) 2.087111175 0.2397513 8.705318218 3.583451e-10 1.5998780
#> z_multi2 0.632076161 0.3949708 1.600311246 1.187819e-01 -0.1706010
#> z_multi3 0.225302890 0.4595353 0.490284219 6.270820e-01 -0.7085851
#> x_c 0.971855697 0.3265662 2.975983428 5.346867e-03 0.3081933
#> z_multi2:x_c -0.164498171 0.4184305 -0.393131454 6.966767e-01 -1.0148512
#> z_multi3:x_c 0.007310125 0.8138866 0.008981748 9.928862e-01 -1.6467064
#> CI Upper DF
#> (Intercept) 2.5743444 34
#> z_multi2 1.4347533 34
#> z_multi3 1.1591909 34
#> x_c 1.6355181 34
#> z_multi2:x_c 0.6858548 34
#> z_multi3:x_c 1.6613267 34
# Stratified estimator with blocks
dat$blockID <- rep(1:5, each = 8)
dat$z_block <- block_ra(blocks = dat$blockID)
lm_lin(y ~ z_block, ~ factor(blockID), data = dat)
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.0704132 0.3451408 5.9987493 1.399160e-06
#> z_block 0.5931938 0.4501499 1.3177696 1.975558e-01
#> (factor(blockID)2)_c 1.1858143 1.1686199 1.0147134 3.183567e-01
#> (factor(blockID)3)_c 1.4533957 1.1962207 1.2149896 2.338464e-01
#> (factor(blockID)4)_c 0.3103012 1.2793724 0.2425417 8.100110e-01
#> (factor(blockID)5)_c 0.6828532 1.1941371 0.5718382 5.716919e-01
#> z_block:(factor(blockID)2)_c -1.5162764 1.4447190 -1.0495303 3.023158e-01
#> z_block:(factor(blockID)3)_c -1.2130004 1.4862041 -0.8161735 4.208346e-01
#> z_block:(factor(blockID)4)_c -0.4459309 1.5448894 -0.2886491 7.748351e-01
#> z_block:(factor(blockID)5)_c -1.9553208 1.3328098 -1.4670666 1.527638e-01
#> CI Lower CI Upper DF
#> (Intercept) 1.3655416 2.775285 30
#> z_block -0.3261349 1.512523 30
#> (factor(blockID)2)_c -1.2008259 3.572455 30
#> (factor(blockID)3)_c -0.9896129 3.896404 30
#> (factor(blockID)4)_c -2.3025258 2.923128 30
#> (factor(blockID)5)_c -1.7559001 3.121606 30
#> z_block:(factor(blockID)2)_c -4.4667862 1.434233 30
#> z_block:(factor(blockID)3)_c -4.2482341 1.822233 30
#> z_block:(factor(blockID)4)_c -3.6010159 2.709154 30
#> z_block:(factor(blockID)5)_c -4.6772816 0.766640 30
if (FALSE) {
# Can also use 'margins' package if you have it installed to get
# marginal effects
library(margins)
lmlout <- lm_lin(y ~ z_block, ~ x, data = dat)
summary(margins(lmlout))
# Can output results using 'texreg'
library(texreg)
texregobj <- extract(lmlout)
}