Clarify covariate adjustment in vignette

DESCRIPTION

@@ -1,6 +1,6 @@
 Package: RDHonest
 Title: Honest Inference in Regression Discontinuity Designs
-Version: 0.9.0
+Version: 1.0.0
 Authors@R:
     c(person(given = "Michal",
             family = "Kolesár",

R/Cbound.R

@@ -40,7 +40,8 @@
 #' }
 #' @examples
 #' ## Subset data to increase speed
-#' r <- RDHonest(log(earnings)~yearat14, data=cghs, subset=abs(yearat14-1947)<10,
+#' r <- RDHonest(log(earnings)~yearat14, data=cghs,
+#'               subset=abs(yearat14-1947)<10,
 #'               cutoff=1947, M=0.04, h=3)
 #' RDSmoothnessBound(r, s=2)
 #' @export

R/RDHonest.R

@@ -71,8 +71,8 @@
 #'     computed according to criterion given by \code{opt.criterion}.
 #' @param weights Optional vector of weights to weight the observations (useful
 #'     for aggregated data). The weights are interpreted as the number of
-#'     observations that each aggregated data point averages over. Disregarded if
-#'     optimal kernel is used.
+#'     observations that each aggregated data point averages over. Disregarded
+#'     if optimal kernel is used.
 #' @param point.inference Do inference at a point determined by \code{cutoff}
 #'     instead of RD.
 #' @param T0 Initial estimate of the treatment effect for calculating the

doc/RDHonest.Rmd

@@ -637,7 +637,7 @@ unadjusted estimate that replaces the original outcome $Y_{i}$ with the
 covariate-adjusted outcome $Y_{i}-W_{i}'\tilde{\gamma}_{Y, h}$. The second
 equality uses the decomposition
 $Y_{i}-W_{i}'\tilde{\gamma}_{Y, h}=\tilde{Y}_{i}-W_{i}'
-(\tilde{\gamma}_{Y h}-\gamma_{Y})$
+(\tilde{\gamma}_{Y, h}-\gamma_{Y})$
 to write the estimator as a sum of the infeasible estimator and a linear
 combination of "placebo RD estimators" $\hat{\tau}_{W_{k}, h}$, that
 replace $Y_{i}$ in the outcome equation with the $k$th element of $W_{i}$,
@@ -673,14 +673,18 @@ of the covariate-adjusted outcome. In our implementation, we first estimate the
 model without covariates (using a rule of thumb to calibrate $M$, the bound on
 the second derivative of $f_{Y}$), and compute the bandwidth $\check{h}$ that's
 MSE optimal without covariates. Based on this bandwidth, we compute a
-preliminary estimate $\check{\gamma}_{Y, \check{h}}$ of $\gamma_{Y}$, and use
-this preliminary estimate to compute the covariate-adjusted outcome
-$Y_{i}-W_{i}'\check{\gamma}_{Y, \check{h}}$. If $\tilde{M}$ is not supplied, we
-calibrate $\tilde{M}$ using the rule of thumb, using this covariate-adjusted
-outcome as the outcome. Similarly, we use this covariate-adjusted outcome as the
-outcome to compute a preliminary estimator of the conditional variance
-$\sigma^{2}_{\tilde{Y}}(x_{i})$, for optimal bandwidth calculations, as in the
-case without covariates.
+preliminary estimate $\tilde{\gamma}_{Y, \check{h}}$ of $\gamma_{Y}$, and use
+this preliminary estimate to compute a preliminary covariate-adjusted outcome
+$Y_{i}-W_{i}'\tilde{\gamma}_{Y, \check{h}}$. If $\tilde{M}$ is not supplied, we
+calibrate $\tilde{M}$ using the rule of thumb, using this preliminary
+covariate-adjusted outcome as the outcome. Similarly, we use this preliminary
+covariate-adjusted outcome as the outcome to compute a preliminary estimator of
+the conditional variance $\sigma^{2}_{\tilde{Y}}(x_{i})$, for optimal bandwidth
+calculations, as in the case without covariates. With this choice of bandwidth
+$h$, in the second step, we estimate $\tau_Y$ using the estimator
+$\tilde{\tau}_{Y, h}$ defined above.
+
+
 
 A demonstration using the `headst` data:
 ```{r}

vignettes/RDHonest.Rmd

@@ -637,7 +637,7 @@ unadjusted estimate that replaces the original outcome $Y_{i}$ with the
 covariate-adjusted outcome $Y_{i}-W_{i}'\tilde{\gamma}_{Y, h}$. The second
 equality uses the decomposition
 $Y_{i}-W_{i}'\tilde{\gamma}_{Y, h}=\tilde{Y}_{i}-W_{i}'
-(\tilde{\gamma}_{Y h}-\gamma_{Y})$
+(\tilde{\gamma}_{Y, h}-\gamma_{Y})$
 to write the estimator as a sum of the infeasible estimator and a linear
 combination of "placebo RD estimators" $\hat{\tau}_{W_{k}, h}$, that
 replace $Y_{i}$ in the outcome equation with the $k$th element of $W_{i}$,
@@ -673,14 +673,18 @@ of the covariate-adjusted outcome. In our implementation, we first estimate the
 model without covariates (using a rule of thumb to calibrate $M$, the bound on
 the second derivative of $f_{Y}$), and compute the bandwidth $\check{h}$ that's
 MSE optimal without covariates. Based on this bandwidth, we compute a
-preliminary estimate $\check{\gamma}_{Y, \check{h}}$ of $\gamma_{Y}$, and use
-this preliminary estimate to compute the covariate-adjusted outcome
-$Y_{i}-W_{i}'\check{\gamma}_{Y, \check{h}}$. If $\tilde{M}$ is not supplied, we
-calibrate $\tilde{M}$ using the rule of thumb, using this covariate-adjusted
-outcome as the outcome. Similarly, we use this covariate-adjusted outcome as the
-outcome to compute a preliminary estimator of the conditional variance
-$\sigma^{2}_{\tilde{Y}}(x_{i})$, for optimal bandwidth calculations, as in the
-case without covariates.
+preliminary estimate $\tilde{\gamma}_{Y, \check{h}}$ of $\gamma_{Y}$, and use
+this preliminary estimate to compute a preliminary covariate-adjusted outcome
+$Y_{i}-W_{i}'\tilde{\gamma}_{Y, \check{h}}$. If $\tilde{M}$ is not supplied, we
+calibrate $\tilde{M}$ using the rule of thumb, using this preliminary
+covariate-adjusted outcome as the outcome. Similarly, we use this preliminary
+covariate-adjusted outcome as the outcome to compute a preliminary estimator of
+the conditional variance $\sigma^{2}_{\tilde{Y}}(x_{i})$, for optimal bandwidth
+calculations, as in the case without covariates. With this choice of bandwidth
+$h$, in the second step, we estimate $\tau_Y$ using the estimator
+$\tilde{\tau}_{Y, h}$ defined above.
+
+
 
 A demonstration using the `headst` data:
 ```{r}