match_y1y0 {MatchGATE}

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 dist function.

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)