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multe.R
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multe.R
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build_matrix <- function(Cm, S) {
if (nlevels(S) > 1) {
cbind(stats::model.matrix(~ S), Cm)
} else {
cbind(rep(1, NROW(Cm)), Cm)
}
}
#' Multiple Treatment Effects Regression
#'
#' Compute contamination bias diagnostics for the partially linear (PL)
#' regression estimator with multiple treatments. Also report four alternative
#' estimators:
#' \describe{
#' \item{OWN}{The own treatment effect component of the PL estimator.}
#' \item{ATE}{The unweighted average treatment effect, implemented using
#' interacted regression.}
#' \item{EW}{Weighted ATE estimator based on easiest-to-estimate weighting (EW)
#' scheme,
#' implemented by running one-treatment-at-a-time regressions.}
#' \item{CW}{Weighted ATE estimator using easiest-to-estimate common
#' weighting (CW) scheme, implemented using weighted regression.}
#' }
#' @param r Fitted model, output of the \code{lm} function.
#' @param treatment_name name of treatment variable
#' @param cluster Factor variable that defines clusters. If \code{NULL} (or not
#' supplied), the command computes heteroscedasticity-robust standard
#' errors, rather than cluster-robust standard errors.
#' @param tol Numerical tolerance for computing LM test statistic for testing
#' variability of the propensity score.
#' @param cw_uniform For the CW estimator, should the target weighting scheme
#' give all comparisons equal weight (if \code{FALSE}), or should it draw
#' from the marginal empirical treatment distribution (if \code{TRUE})?
#' @return Returns a list with the following components: \describe{
#'
#' \item{est_f}{Data frame with alternative estimators and standard errors for
#' the full sample}
#'
#' \item{est_o}{Data frame with alternative estimators and standard errors for
#' the overlap sample}
#'
#' \item{cb_f, cb_0}{Data frame with differences between PL and alternative
#' estimators, along with standard errors for the full, and for the overlap
#' sample.}
#'
#' \item{n_f, n_o}{Sample sizes for the full, and for the overlap sample.}
#'
#' \item{k_f, k_o}{Number of controls for the full, and for the overlap sample.}
#'
#' \item{t_f, t_o}{LM and Wald statistic, degrees of freedom, and p-values for
#' the full and for the overlap sample, for testing the hypothesis of no
#' variation in the propensity scores.}
#'
#' \item{pscore_sd_f, pscore_sd_o}{Standard deviation of the estimated
#' propensity score in the full and overlap samples.}
#'
#' \item{Y, X, wgt}{Vector of outcomes, treatments and weights in the overlap
#' sample}
#'
#' \item{Zm}{Matrix of controls in the overlap sample}
#' }
#' @references{
#'
#' \cite{Paul Goldsmith-Pinkham, Peter Hull, and Michal Kolesár. Contamination
#' bias in linear regressions. ArXiv:2106.05024, February 2024.}
#' }
#' @examples
#' wbh <- fl[fl$race=="White" | fl$race=="Black" | fl$race=="Hispanic", ]
#' wbh <- droplevels(wbh)
#' r1 <- stats::lm(std_iq_24~race+factor(age_24)+female, weight=W2C0, data=wbh)
#' m1 <- multe(r1, treatment="race")
#' @export
multe <- function(r, treatment_name, cluster=NULL, tol=1e-7, cw_uniform=FALSE) {
Y <- stats::model.response(r$model)
wgt <- stats::model.weights(r$model)
X <- r$model[, treatment_name]
## Find factor variable with greatest number of levels
nl <- vapply(r$model, nlevels, numeric(1))
nl[treatment_name] <- 0
if (max(nl) > 0) {
stratum_name <- names(which.max(nl))
S <- r$model[, stratum_name]
} else {
stratum_name <- "(Intercept)"
S <- factor(rep(1, length(X)))
}
coefnames <- names(stats::coefficients(r))
filter <- (coefnames=="(Intercept)") |
coefnames %in% paste0(treatment_name,
levels(r$model[[treatment_name]])) |
coefnames %in% paste0(stratum_name,
levels(r$model[[stratum_name]])) |
unname(is.na(r$coefficients))
if (sum(is.na(r$coefficients)) > 0) {
message("These columns are dropped due to collinearity: ",
paste(names(r$coefficients)[is.na(r$coefficients)],
collapse=", "))
}
Cm <- stats::model.matrix(r)[, !filter, drop=FALSE]
if (NCOL(build_matrix(Cm, S))==1) {
stop("There are no controls beyond the intercept")
}
if (!is.null(wgt) && any(wgt == 0)) {
ok <- wgt != 0
Y <- Y[ok]
X <- X[ok]
Cm <- Cm[ok, , drop=FALSE]
S <- droplevels(S[ok])
wgt <- wgt[ok]
cluster <- cluster[ok]
}
r1 <- decomposition(Y, X, build_matrix(Cm, S), wgt, cluster, tol,
cw_uniform)
n1 <- length(Y)
k1 <- NCOL(build_matrix(Cm, S))-1L
## 1. Drop strata with no overlap
idx <- vector(length=0)
if (nlevels(S) > 1) {
dropstrata <- levels(S)[colSums(table(X, S)==0)>0]
idx <- S %in% dropstrata
if (sum(idx)> 0) {
message("For variable ", stratum_name,
" the following levels fail overlap:\n",
paste(dropstrata, collapse=", "),
"\nDropping observations with these levels")
}
Y <- Y[!idx]
X <- X[!idx]
Cm <- Cm[!idx, , drop=FALSE]
S <- droplevels(S[!idx])
wgt <- wgt[!idx]
cluster <- cluster[!idx]
}
## 2. Drop controls that don't have within-treatment variation
Zm <- build_matrix(Cm, S)
rs <- function(x) {
qrz <- qr(Zm[X==x, ])
qrz$pivot[-seq.int(qrz$rank)]
}
dropctrl <- unique(unlist(lapply(levels(X), rs)))
if (sum(dropctrl)> 0) {
message("\nThe following variables have no within-treatment variation",
" and are dropped:\n",
paste(colnames(Zm)[sort(dropctrl)], collapse=", "))
Zm <- Zm[, -dropctrl]
}
r2 <- list()
n2 <- k2 <- NA
if (length(Y)==0) {
message("Overlap sample is empty")
} else if (sum(dropctrl) > 0 || sum(idx) > 0) {
r2 <- decomposition(Y, X, Zm, wgt, cluster, tol, cw_uniform)
n2 <- length(Y)
k2 <- NCOL(Zm)-1L
}
structure(list(est_f=r1$A, est_o=r2$A, cb_f=r1$B, cb_o=r2$B, n_f=n1,
n_o=n2, k_f=k1, k_o=k2, t_f=r1$tests, t_o=r2$tests,
pscore_sd_f = r1$pscore_sd, pscore_sd_o = r2$pscore_sd,
Y=Y, X=X, Zm=Zm, wgt=wgt), class="multe")
}
#' @export
print.multe <- function(x, digits=getOption("digits"), ...) {
cat("Estimates on full sample:\n")
oracle <- (seq.int(nrow(x$est_f)/3)-1)*3+3
rownames(x$est_f)[oracle-1] <- rep("SE", length(oracle))
print(x$est_f[-oracle, ], digits=digits)
if (!is.null(x$est_o)) {
rownames(x$est_o)[oracle-1] <- rep("SE", length(oracle))
cat("\nEstimates on overlap sample:\n")
print(x$est_o[-oracle, ], digits=digits)
}
cat("\nP-values for null hypothesis of no propensity score variation:\n")
cat("Wald test:", round(x$t_f$p_W, digits=digits))
cat(", LM test:", round(x$t_f$p_LM, digits=digits), "\n")
cat("\nSD(estimated propensity score), maximum over treatment arms:\n")
cat("Full sample:", round(max(x$pscore_sd_f), digits=digits))
if (!is.null(x$pscore_sd_o))
cat(", Overlap sample:", round(max(x$pscore_sd_o), digits=digits))
cat("\n")
}