estate: Estimation of average treatment effects

Description

Function for estimating the average treatment effect (ATE). Permits regression adjustment for covariates, difference estimation (with a pretreatment measure of the outcome variable), inverse probability weighting, and unbiased Horvitz-Thompson estimation.

Usage

estate(Y, Z, X = NULL, Ypre = NULL, prob = NULL, HT = FALSE)

Arguments

numeric vector of length N, outcome variable

binary vector (0 or 1) of length N, treatment indicator

N-by-k numeric matrix of covariates for regression adjustment

Ypre

numeric vector of length N, pretreatment measure of the outcome variable for difference estimation

prob

numeric vector within the (0,1) interval of length N, probability of treatment assignment, as outputted by genprob() or genprobexact(). When prob=NULL (the default), assumes uniform probability of assignment to treatment equal to the mean of Z

when HT=TRUE, invokes the Horvitz-Thompson (difference-in-totals) estimator. When HT=FALSE, invokes the inverse-probability-weighted regression estimator

Value

a scalar, the estimated average treatment effect

References

Peter M. Aronow and Joel A. Middleton. 2012. A Class of Unbiased Estimators of the Average Treatment Effect in Randomized Experiments. Working paper, Yale University. http://pantheon.yale.edu/~pma5/unbiasedestimators.pdf

Gerber, Alan S. and Donald P. Green. 2012. Field Experiments: Design, Analysis, and Interpretation. New York: W.W. Norton.

Horvitz, D.G. and D.J. Thompson. 1952. A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc. 47 663-684.

Examples

Run this code

y <- c(8,6,2,0,3,1,1,1,2,2,0,1,0,2,2,4,1,1) 
Z <- c(1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0)
cluster <- c(1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9)
block <- c(rep(1,4),rep(2,6),rep(3,8))

probs <- genprobexact(Z,blockvar=block, clustvar=cluster) # probability of treatment
ate <- estate(y,Z,prob=probs) # estimate the ATE

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