get_ipw_scores {maq}

Construct evaluation scores via inverse-propensity weighting.

Description

A simple convenience function to construct an evaluation score matrix via IPW, where entry (i, k) equals

• \frac{\mathbf{1}(W_i=k)Y_i}{P[W_i=k | X_i]} - \frac{\mathbf{1}(W_i=0)Y_i}{P[W_i=0 | X_i]},

where W_i is the treatment assignment of unit i and Y_i the observed outcome. k = 1 \ldots K are one of K treatment arms and k = 0 is the control arm.

Usage

get_ipw_scores(Y, W, W.hat = NULL)

Arguments

Y

The observed outcome.

W

The observed treatment assignment (must be a factor vector, where the first factor level is the control arm).

W.hat

Optional treatment propensities. If these vary by unit and arm, then this should be a matrix with the treatment assignment probability of units to arms, with columns corresponding to the levels of W. If these only vary by arm, a vector can also be supplied. If W.hat is NULL (Default), then the assignment probabilities are assumed to be uniform and the same for each arm.

Value

An n \cdot K matrix of evaluation scores.

Examples

# Draw some equally likely samples from control arm A and treatment arms B and C.
n <- 5000
W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE))
Y <- 42 * (W == "B") - 42 * (W == "C") + rnorm(n)
IPW.scores <- get_ipw_scores(Y, W)
# An IPW-based estimate of E[Y(B) - Y(A)] and E[Y(C) - Y(A)]. Should be approx 42 and -42.
colMeans(IPW.scores)

# Draw non-uniformly from the different arms.
W.hat <- c(0.2, 0.2, 0.6)
W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE, prob = W.hat))
Y <- 42 * (W == "B") - 42 * (W == "C") + rnorm(n)
IPW.scores <- get_ipw_scores(Y, W, W.hat = W.hat)
# Should still be approx 42 and -42.
colMeans(IPW.scores)