| Title: | Estimate Group Average Treatment Effects with Matching |
| Version: | 0.0.10 |
| Description: | Two novel matching-based methods for estimating group average treatment effects (GATEs). The match_y1y0() and match_y1y0_bc() functions are used for imputing the potential outcomes based on matching and bias-corrected matching techniques, respectively. The EstGATE() function is employed to estimate the GATE after imputing the potential outcomes. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.1 |
| Imports: | locpol, stats |
| NeedsCompilation: | no |
| Packaged: | 2024-04-07 06:19:52 UTC; dell |
| Author: | Zhaoqing Tian 
[aut, cre, com],
Peng Wu [aut,
ths],
Yilin Chen [dtc] |
| Maintainer: | Zhaoqing Tian <tzqluck@163.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-04-08 15:10:05 UTC |
Estimating Group Average Treatment Effects
Description
When imputed values for Y^1 and Y^0 are available
for each individual, we can use EstGATE to estimate the
group average treatment effects (GATE) defined by
GATE(z) = E[Y^1 - Y^0 | Z=z]
for some for possible values z of Z.
Usage
EstGATE(Y1_Y0, Z, Zeval, h)
Arguments
Y1_Y0 |
A vector in which each element is a treatment effect for each individual. |
Z |
A subvector of the covariates |
Zeval |
Vector of evaluation points of |
h |
A smoothing parameter, bandwidth. |
Value
The value of the corresponding GATE at different evaluation points.
Examples
set.seed(691)
n <- 2000
X1 <- runif(n, -0.5,0.5)
X2 <- rnorm(n, sd = 0.5)
X = cbind(X1, X2)
A = sample(c(0,1), n, TRUE)
Y0 <- X2 + X1*X2/2 + rnorm(n, sd = 0.25)
Y1 <- A * (2*X1^2) + X2 + X1*X2/2 + rnorm(n, sd = 0.25)
Y <- A * Y1 + (1-A)*Y0
res.match <- match_y1y0(X, A, Y, K = 5)
y1_y0 <- res.match$Y1 - res.match$Y0
Z <- X1
Zeval = seq(min(Z), max(Z), len = 101)
h <- 0.5 * n^(-1/5)
res <- EstGATE(Y1_Y0 = y1_y0, Z, Zeval, h = h)
plot(x = Zeval, y = 2*Zeval^2,
type = "l", xlim = c(-0.6, 0.5),
main = "Estimated value vs. true value",
xlab = "Zeval", ylab = "GATE",
col = "DeepPink", lwd = "2")
lines(x = res$Zeval, y = res$GATE,
col="DarkTurquoise", lwd = "2")
legend('bottomleft', c("Estimated GATE","True GATE"),
col=c("DarkTurquoise","DeepPink"),
text.col=c("DarkTurquoise","DeepPink"), cex = 0.8)
Imputing Missing Potential Outcomes with Matching
Description
Impute missing potential outcomes for each individual with matching.
Usage
match_y1y0(X, A, Y, K = 5, method = "euclidean")
Arguments
X |
A matrix representing covariates, where each row represents the value of a different covariates for an individual. |
A |
A vector representing the treatment received by each individual. |
Y |
A vector representing the observed outcome for each individual. |
K |
When imputing missing potential outcomes, the average number of similar individuals are taken based on covariates similarity. |
method |
The distance measure to be used. It is a argument embed in
|
Details
Here are the implementation details for the imputation processes.
Denote \hat{Y}^0_i and \hat{Y}^1_i as the imputed potential
outcomes for individual i. Without loss of generality, if A_i = 0, then
\hat{Y}^0_i = Y_i, and \hat{Y}^1_i is the average of outcomes for the K units that are the most
similar to the individual i, i.e.,
\hat{Y}_i^0 = \frac 1 K \sum_{j\in\mathcal{J}_K(i)}Y_j,
where \mathcal{J}_K(i) represents the set of K matched individuals
with A_i = 1, that are the closest to the individual i in terms of
covariates similarity, and vice versa.
Value
Returns a matrix of completed matches, where each row is the imputed (Y^1, Y^0)
for each individual.
Examples
n <- 100
p <- 2
X <- matrix(rnorm(n*p), ncol = p)
A <- sample(c(0,1), n, TRUE)
Y <- A * (2*X[,1]) + X[,2]^2 + rnorm(n)
match_y1y0(X = X, A = A, Y = Y, K =5)
Imputing Missing Potential Outcomes with Bias-Corrected Matching
Description
Impute missing potential outcomes for each individual with bias-corrected matching.
Usage
match_y1y0_bc(X, A, Y, miu1.hat, miu0.hat, K = 5, method = "euclidean")
Arguments
X |
A matrix representing covariates, where each row represents the value of a different covariates for an individual. |
A |
A vector representing the treatment received by each individual. |
Y |
A vector representing the observed outcome for each individual. |
miu1.hat |
The estimated outcome regression function for |
miu0.hat |
The estimated outcome regression function for |
K |
When imputing missing potential outcomes, the average number of similar individuals are taken based on covariates similarity. |
method |
The distance measure to be used. It is a argument embed in
|
Details
Here are the implementation details for the imputation processes.
Denote \hat{Y}^0_i and \hat{Y}^1_i as the imputed potential
outcomes for individual i. For example, if A_i = 0, then \hat{Y}^0_i = Y^0_i.
However, for obtaining \hat{Y}^1_i, we require to introduce an outcome
regression function \mu_1(X) for Y^1. Let \hat{\mu}_1(X) be the fitted value of
\mu_1(X), then \hat{Y}^1_i is defined as follows,
\hat{Y}_i^1 = \frac 1 K \sum_{j\in\mathcal{J}_K(i)}\{Y_j+
\hat{\mu}_1(X_i)-\hat{\mu}_1(X_j)\},
where \mathcal{J}_K(i) represents the set of K matched individuals
with A_i = 1, that are the closest to the individual i in terms of
covariates similarity, and vice versa.
Value
Returns a matrix of completed matches, where each row is the imputed (Y^1, Y^0)
for each individual.
Examples
n = 100
X1 <- runif(n, -0.5,0.5)
X2 <- sample(c(0,1,2), n, TRUE)
X = cbind(X1, X2)
A = sample(c(0,1), n, TRUE)
Y = A * (2*X1) + X1 + X2^2 + rnorm(n)
miu1_hat <- cbind(1,X) %*% as.matrix(lm(Y ~ X, subset = A==1)$coef)
miu0_hat <- cbind(1,X) %*% as.matrix(lm(Y ~ X, subset = A==0)$coef)
match_y1y0_bc(X = X, A = A, Y = Y, miu1.hat = miu1_hat,
miu0.hat = miu0_hat, K = 5)