DR scores outside of 0-1 for binary outcomes
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Thank you for the package! I'm trying to estimate double robust scores for a binary outcome variable. However, when using double_robust_scores(), I get gamma values outside of 0-1. I can reproduce this with the example in the package but a binary outcome variable.
# library(policytree)
n <- 250
p <- 10
X <- matrix(rnorm(n * p), n, p)
W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE))
Y <- sample(c(0, 1), n, replace = TRUE) # new outcome variable
multi.forest <- grf::multi_arm_causal_forest(X, Y, W)
# Compute doubly robust reward estimates.
Gamma.matrix <- double_robust_scores(multi.forest)
summary(Gamma.matrix)
A B C
Min. :-1.2928 Min. :-1.8635 Min. :-1.3356
1st Qu.: 0.4616 1st Qu.: 0.5229 1st Qu.: 0.3900
Median : 0.4968 Median : 0.5512 Median : 0.4283
Mean : 0.4956 Mean : 0.5451 Mean : 0.4237
3rd Qu.: 0.5376 3rd Qu.: 0.5911 3rd Qu.: 0.4581
Max. : 2.4399 Max. : 2.4520 Max. : 2.6737
That's right; the DR scores used with AIPW are not bounded within the range of the Y. This is simply a consequence of how DR scores are obtained; and doing something direct like thresholding DR scores into the range of the data might actually bias the algorithm.
There are other alternatives to AIPW that avoid this unboundedness issue; see, e.g., the following. However, that's not what's implemented/used here.
Tan, Zhiqiang. "Bounded, efficient and doubly robust estimation with inverse weighting." Biometrika 97.3 (2010): 661-682.