CBPS (version 0.23)

AsyVar: Asymptotic Variance and Confidence Interval Estimation of the ATE

Description

AsyVar estimates the asymptotic variance of the ATE obtained with the CBPS or oCBPS method. It also returns the finite variance estimate, the finite standard error, and a CI for the ATE.

Usage

AsyVar(
  Y,
  Y_1_hat = NULL,
  Y_0_hat = NULL,
  CBPS_obj,
  method = "CBPS",
  X = NULL,
  TL = NULL,
  pi = NULL,
  mu = NULL,
  CI = 0.95
)

Arguments

Y

The vector of actual outcome values (observations).

Y_1_hat

The vector of estimated outcomes according to the treatment model. (AsyVar automatically sets the treatment model as a linear regression model and it is fitted within the function.) If CBPS_obj is specified, or if X \(and\) TL are specified, this is unnecessary.

Y_0_hat

The vector of estimated outcomes according to the control model. (AsyVar automatically sets the control model as a linear regression model and it is fitted within the function.) If CBPS_obj is specified, or if X \(and\) TL are specified, this is unnecessary.

CBPS_obj

An object obtained with the CBPS function. If this object is not sepecified, then X, TL, pi, and mu must \(all\) be specified instead.

method

The specific method to be considered. Either "CBPS" or "oCBPS" must be selected.

X

The matrix of covariates with the rows corresponding to the observations and the columns corresponding to the variables. The left most column must be a column of 1's for the intercept. (X is not necessary if CBPS_obj is specified.)

TL

The vector of treatment labels. More specifically, the label is 1 if it is in the treatment group and 0 if it is in the control group. (TL is not necessary if CBPS_obj is specified.)

pi

The vector of estimated propensity scores. (pi is not necessary if CBPS_obj is specified.)

mu

The estimated average treatment effect obtained with either the CBPS or oCBPS method. (mu is not necessary if CBPS_obj is specified.)

CI

The specified confidence level (between 0 and 1) for calculating the confidence interval for the average treatment effect. Default value is 0.95.

Value

mu.hat

The estimated average treatment effect, \(hat{\mu}\).

asy.var

The estimated asymptotic variance of \(\sqrt{n}*hat{\mu}\) obtained with the CBPS or oCBPS method.

var

The estimated variance of \(hat{\mu}\) obtained with the CBPS or oCBPS method.

std.err

The standard error of \(hat{\mu}\) obtained with the CBPS or oCBPS method.

CI.mu.hat

The confidence interval of \(hat{\mu}\) obtained with the CBPS or oCBPS method with the confidence level specified in the input argument.

References

Fan, Jianqing and Imai, Kosuke and Lee, Inbeom and Liu, Han and Ning, Yang and Yang, Xiaolin. 2021. ``Optimal Covariate Balancing Conditions in Propensity Score Estimation.'' Journal of Business & Economic Statistics. https://imai.fas.harvard.edu/research/CBPStheory.html

Examples

# NOT RUN {
#GENERATING THE DATA
n=300
          
#Initialize the X matrix.
X_v1 <- rnorm(n,3,sqrt(2))
X_v2 <- rnorm(n,0,1)
X_v3 <- rnorm(n,0,1)
X_v4 <- rnorm(n,0,1)
X_mat <- as.matrix(cbind(rep(1,n), X_v1, X_v2, X_v3, X_v4)) 
          
#Initialize the Y_1 and Y_0 vector using the treatment model and the control model.
Y_1 <- X_mat %*% matrix(c(200, 27.4, 13.7, 13.7, 13.7), 5, 1) + rnorm(n)
Y_0 <- X_mat %*% matrix(c(200, 0 , 13.7, 13.7, 13.7), 5, 1) + rnorm(n)
          
#True Propensity Score calculation.
pre_prop <- X_mat[,2:5] %*% matrix(c(0, 0.5, -0.25, -0.1), 4, 1)
propensity_true <- (exp(pre_prop))/(1+(exp(pre_prop)))
          
#Generate T_vec, the treatment vector, with the true propensity scores.
T_vec <- rbinom(n, size=1, prob=propensity_true)
          
#Now generate the actual outcome Y_outcome (accounting for treatment/control groups).
Y_outcome <- Y_1*T_vec + Y_0*(1-T_vec)
          
#Use oCBPS.
ocbps.fit <- CBPS(T_vec ~ X_mat, ATT=0, baseline.formula = ~X_mat[,c(1,3:5)], 
                 diff.formula = ~X_mat[,2])
          
#Use the AsyVar function to get the asymptotic variance of the 
#estimated average treatment effect and its confidence interval when using oCBPS.
AsyVar(Y=Y_outcome, CBPS_obj=ocbps.fit, method="oCBPS", CI=0.95)

#Use CBPS.
cbps.fit <- CBPS(T_vec ~ X_mat, ATT=0)

#Use the AsyVar function to get the asymptotic variance of the
#estimated average treatment effect and its confidence interval when using CBPS.
AsyVar(Y=Y_outcome, CBPS_obj=cbps.fit, method="CBPS", CI=0.95)

# }