Estimates the average causal effect using IPW with a logistic propensity score model.
Arguments
- theta
Numeric vector of length
3 + b, wherebis the number of propensity score model parameters.- y
Numeric vector of n observed outcomes.
- A
Numeric vector of n binary treatment indicators (0/1).
- W
Numeric n-by-b design matrix for the propensity score model.
- truncate
Optional length-2 numeric vector
c(lower, upper)to clip estimated propensity scores. Bounds must be in ascending order (lower <= upper). DefaultNULL.- weights
Optional numeric vector of n weights. Default
NULL.
Value
A (3+b)-by-n matrix of estimating equation contributions, with
the first three rows named ACE, E[Y^1], and E[Y^0] and the propensity
score rows named W_1 through W_b for the columns of W.
Examples
# A binary treatment, two confounders, and a continuous outcome whose true
# average causal effect is 1.5.
set.seed(42)
n <- 1000
W1 <- rnorm(n)
W2 <- rbinom(n, 1, 0.4)
A <- rbinom(n, 1, inverse_logit(-0.5 + 0.5 * W1 + 0.3 * W2))
Y <- 2 + 1.5 * A + W1 - 0.5 * W2 + rnorm(n)
W_ps <- cbind(1, W1, W2) # Propensity score design matrix
psi <- function(theta) ee_ipw(theta, y = Y, A = A, W = W_ps)
# theta holds the average causal effect, the mean under treatment, and the
# mean under no treatment, followed by the three propensity score
# coefficients.
m <- m_estimate(stacked_equations = psi, init = rep(0, 6))
coef(m)[1:3]
#> ACE E[Y^1] E[Y^0]
#> 1.575945 3.313529 1.737584