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Additive robust regression on LASSO-selected covariates

Source: R/fit_lasso.R
lm_robust_lasso.Rd

Runs lasso_select_covariates and fits lm_robust with the selected covariates entered additively, that is outcome ~ treatment + X1 + X2.

Usage

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

Arguments

formula

A two-sided formula outcome ~ treatment.

covariates

Candidate covariates: a one-sided formula, a character vector of column names, or a bare expression.

data

A data frame.

weights, subset, clusters, se_type, ci, alpha, return_vcov, try_cholesky

Passed through to lm_lin or lm_robust.

lasso_args

A named list of further arguments for lasso_select_covariates, such as lambda_rule or seed.

Value

An lm_robust object, carrying the attributes described in adjustment.

Details

Additive adjustment assumes a common covariate slope across arms. That assumption buys degrees of freedom relative to lm_lin_lasso, which fits a slope per arm, and it is what makes this the right choice when arms are small enough that the interacted model is unstable. When it is wrong, the treatment coefficient is no longer guaranteed to be consistent for the average treatment effect, which is the reason Lin (2013) recommends the interacted form as the default. Choose deliberately.

Fallback

lm_lin cannot be fitted with no covariates, and an adjusted fit can come back degenerate when the selected set is nearly collinear within an arm. In either case this function returns an unadjusted lm_robust fit, which for a binary treatment is the difference in means. Because that substitution changes the specification, it is recorded rather than hidden: read it back with adjustment and selected_covariates. The specific triggers are that selection returned ~1, that lm_lin threw, or that the treatment row of the adjusted fit has a non-finite standard error.

References

Lin, W. (2013). Agnostic notes on regression adjustments to experimental data: reexamining Freedman's critique. Annals of Applied Statistics, 7(1), 295-318. doi:10.1214/12-AOAS583

See also

lm_lin_lasso for arm-specific slopes.

Other adjusted estimators: lm_lin_lasso(), lm_moderator_lasso()

Examples

set.seed(1)
n <- 400
dat <- data.frame(Z = rep(0:1, n / 2), X1 = rnorm(n), X2 = rnorm(n))
dat$Y <- 0.5 * dat$Z + 1.5 * dat$X1 + rnorm(n)

fit <- lm_robust_lasso(Y ~ Z, ~ X1 + X2, data = dat)
adjustment(fit)
#> [1] "robust"