# late.aipw: Augmented inverse probability weighted estimation of local... In RCAL: Regularized Calibrated Estimation

## Description

This function implements augmented inverse probability weighted (IPW) estimation of local average treatment effects (LATEs) as proposed in Tan (2006), provided the fitted instrument propensity scores and fitted values from both treatment and outcome regressions.

## Usage

 1 late.aipw(y, tr, iv, mfp, mft, mfo, off = NULL) 

## Arguments

 y An n x 1 vector of observed outcomes. tr An n x 1 vector of treatment indicators (=1 if treated or 0 if untreated). iv An n x 1 vector of instruments (0 or 1). mfp An n x 2 matrix of fitted instrument propensity scores for iv=0 (first column) and iv=1 (second column). mft An n x 2 matrix of fitted values from treatment regression, for iv=0 (first column) and iv=1 (second column). mfo An n x 4 matrix of fitted values from outcome regression, for iv=0, tr=0 (first column), iv=0, tr=1 (second column), iv=1, tr=0 (third column) and iv=1, tr=1 (fourth column). off A 2 x 1 vector of offset values (e.g., the true values in simulations) used to calculate the z-statistics.

## Details

The individual expectations θ_d=E(Y(d)|D(1)>D(0)) are estimated separately for d\in\{0,1\} using inverse probability weighting ("ipw"), treatment and outcome regressions ("or") and augmented IPW methods as proposed in Tan (2006). The population LATE is defined as θ_1-θ_0.

## Value

 ipw A 2 x 1 vector of IPW estimates of θ_1 and θ_0; see Details. or A 2 x 1 vector of regression estimates of θ_1 and θ_0; see Details. est A 2 x 1 vector of augmented IPW estimates of θ_1 and θ_0; see Details. var The estimated variances associated with the augmented IPW estimates of θ_1 and θ_0. ze The z-statistics for the augmented IPW estimates of θ_1 and θ_0, compared to off. late.est The augmented IPW estimate of LATE. late.var The estimated variance associated with the augmented IPW estimate of LATE. late.ze The z-statistic for the augmented IPW estimate of LATE, compared to off.

## References

Tan, Z. (2006) Regression and weighting methods for causal inference using instrumental variables, Journal of the American Statistical Association, 101, 1607<e2><80><93>1618.

RCAL documentation built on Nov. 8, 2020, 4:22 p.m.