lm_lin: Linear regression with the Lin (2013) covariate adjustment
In estimatr: Fast Estimators for Design-Based Inference

lm_lin

R Documentation

Linear regression with the Lin (2013) covariate adjustment

Description

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).

Usage

lm_lin(
  formula,
  covariates,
  data,
  weights,
  subset,
  clusters,
  se_type = NULL,
  ci = TRUE,
  alpha = 0.05,
  return_vcov = TRUE,
  try_cholesky = FALSE
)

Arguments

`formula`	an object of class formula, as in `lm`, such as `Y ~ Z` with only one variable on the right-hand side, the treatment
`covariates`	a right-sided formula with pre-treatment covariates on the right hand side, such as `~ x1 + x2 + x3`.
`data`	A `data.frame`
`weights`	the bare (unquoted) names of the weights variable in the supplied data.
`subset`	An optional bare (unquoted) expression specifying a subset of observations to be used.
`clusters`	An optional bare (unquoted) name of the variable that corresponds to the clusters in the data.
`se_type`	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.
`ci`	logical. Whether to compute and return p-values and confidence intervals, TRUE by default.
`alpha`	The significance level, 0.05 by default.
`return_vcov`	logical. Whether to return the variance-covariance matrix for later usage, TRUE by default.
`try_cholesky`	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)

Details

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.

Value

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:

`coefficients`	the estimated coefficients
`std.error`	the estimated standard errors
`statistic`	the t-statistic
`df`	the estimated degrees of freedom
`p.value`	the p-values from a two-sided t-test using `coefficients`, `std.error`, and `df`
`conf.low`	the lower bound of the `1 - alpha` percent confidence interval
`conf.high`	the upper bound of the `1 - alpha` percent confidence interval
`term`	a character vector of coefficient names
`alpha`	the significance level specified by the user
`se_type`	the standard error type specified by the user
`res_var`	the residual variance
`N`	the number of observations used
`k`	the number of columns in the design matrix (includes linearly dependent columns!)
`rank`	the rank of the fitted model
`vcov`	the fitted variance covariance matrix
`r.squared`	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.
`adj.r.squared`	The `R^2` but penalized for having more parameters, `rank`
`weighted`	whether or not weights were applied
`call`	the original function call
`fitted.values`	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).

References

Freedman, David A. 2008. "On Regression Adjustments in Experiments with Several Treatments." The Annals of Applied Statistics. JSTOR, 176-96. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/12-AOAS583")}.

Examples

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)

# Works with multiple pre-treatment covariates
lm_lin(y ~ z, covariates = ~ x + x2, data = dat)

# Also centers data AFTER evaluating any functions in formula
lmlin_out2 <- lm_lin(y ~ z, covariates = ~ x + log(x3), data = dat)
lmlin_out2$scaled_center["log(x3)"]
mean(log(dat$x3))

# 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)

# 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)

# 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)

## Not run: 
  # 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)

## End(Not run)

estimatr documentation built on May 29, 2024, 7:23 a.m.