Each level gets its OWN clever covariate 1{A = a}/g_a(W) and its own
fluctuation, because one logistic update cannot solve L score
equations at once. min_g exposes levels with almost no support.
A holds one-based level labels.
Usage
Tmlecat(Y, A, Q, G, ref = 1, gbound = 0.025, level = 0.95)
Arguments
- Y
Outcome in [0, 1].
- A
One-based treatment level of each observation.
- Q
Initial E[Y | A = a, W], one column per level.
- G
Initial P(A = a | W), rows summing to 1.
- ref
One-based reference level for the contrasts.
- gbound
Truncation applied to each g_a.
- level
Confidence level.
Value
List with psi, se, contrast,
contrast_se, ci_lower, ci_upper, min_g,
ref, n, L.
Details
Formula: for each level a, fluctuate logit Q(a,W) on
H_a = 1{A = a}/g_a(W); psi_a = mean(Q*(a,W))
References
Verified against the CRAN package tmle 2.1.1 (Gruber & van
der Laan); the multi-level extension applies the same fluctuation per
level, as in van der Laan & Rose (2011), Targeted Learning, Chapter 4.
Examples
set.seed(13)
n <- 300
A <- sample(1:3, n, TRUE)
Y <- rbinom(n, 1, c(0.3, 0.5, 0.6)[A])
Q <- matrix(rep(c(0.3, 0.5, 0.6), each = n), n) # initial fits per level
G <- matrix(1 / 3, n, 3)
Tmlecat(Y, A, Q, G)$psi
#> [1] 0.3142857 0.4831461 0.5943396
