MB: Mahalanobis balancing

In yimindai0521/MBalance: Mahalanobis balancing: a multivariate perspective on approximate covariate balancing

Mahalanobis balancing

Description

Mahalanobis balancing is a multivariate perspective of approximate covariate balancing method to estimate average treatment effect.

Usage

MB(
  x,
  treat,
  group1,
  group2 = NA,
  outcome,
  method = "MB",
  delta.space = c(0.1, 0.01, 0.001, 1e-04, 1e-05, 1e-06),
  iterations = 1000
)

Arguments

x	covariates.
treat	treatment indicator vector.
group1	see Details.
group2	see Details, Default: NA.
outcome	outcome vector.
method	a string that takes values in "MB", "MB2", "kernelMB". See Details. Default: 'MB'.
delta.space	tuning parameter in balancing. See Details. Default: c(1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6).
iterations	iteration time in optimization problem, Default: 1000.

Details

group1 and group0

• To estimate E(Y (1)) (average treatment effect for group 1), you need to set group1 = 1 and ignore group2. Similarly, To estimate E(Y (0)) (average treatment effect for group 0), you need to set group1 = 0 and ignore group2.

• To estimate average treatment effect on the control group E(Y (1) | T = 0), you need to set group1 = 1 and group2 = 0. Similarly, To estimate average treatment effect on the treated group E(Y (0) | T = 1), you need to set group1 = 0 and group2 = 1.

• This function is feasible when there are more than two groups.

method can be a valid string, including

• "MB": We choose the weighting matrix {W}_1=[diag(\hat{Σ})]^{-1} where \hat{Σ} denotes sample covariance matrix.

• "MB2": We choose the weighting matrix {W}_2={[\hat{Σ}]^{-1}} where \hat{Σ} denotes sample covariance matrix.

• "kernelMB": Firstly, we modify our covariate to X_i* = (Φ(X_1,X_i), ..., Φ(X_n,X_i)), then we apply method "MB" to produce Mahalanobis balancing weights.

delta.space grid of values for the tuning parameter, a vector of candidate values for the degree of approximate covariate balance. The default is c(1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6).

Value

a MB object with the following attributes:

• AT: the estimate of average treatment effect in group1 (i.e, E(Y(group1))).

• weight: the estimated Mahalanobis balancing weight.

• GMIM: Generalized Multivariate Imbalance Measure that defines in our paper.

• delta: the tuning parameter we choose.

Examples

##estimating ATE##
set.seed(0521)
data        <- si.data()
result1     <- MB(x = data$X, treat = data$Tr, group1 = 1, outcome = data$Y, method = "MB")
result2     <- MB(x = data$X, treat = data$Tr, group1 = 0, outcome = data$Y, method = "MB")

##an estimate of ATE
result1$AT - result2$AT

##estimating ATC##
result3     <- MB(x = data$X, treat = data$Tr, group1 = 1, group2 = 0, outcome = data$Y, method = "MB")

##an estimate of ATC
result3$AT - mean(data$Y[data$Tr == 0])

yimindai0521/MBalance documentation built on May 9, 2022, 4:06 p.m.