This function implements inverse probability weighted (IPW) estimation of average treatment effects (ATEs), provided fitted propensity scores.
ate.ipw(y, tr, mfp)
An \(n\) x \(1\) vector of observed outcomes.
An \(n\) x \(1\) vector of treatment indicators (=1 if treated or 0 if untreated).
An \(n\) x \(2\) matrix of fitted propensity scores for untreated (first column) and treated (second column).
The direct IPW estimates of 1.
The ratio IPW estimates of means.
The ratio IPW estimate of ATE.
Tan, Z. (2020a) Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data, Biometrika, 107, 137<U+2013>158.
Tan, Z. (2020b) Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data, Annals of Statistics, 48, 811<U+2013>837.