Inverse probability tilting — bw

bw_ipt() specifies inverse probability tilting for balance(). A propensity model is fit not by maximum likelihood but by a tilted moment condition that forces each treatment group's weighted covariate means to their estimand targets, so balance on the requested moments is exact by construction. Inverse probability tilting supports binary and categorical exposures.

Usage

bw_ipt(
  ...,
  link = c("logit", "probit", "cloglog"),
  convergence_tolerance = 1e-10,
  max_iterations = NULL
)

Arguments

...: Reserved for future extensions; must be empty. Tuning parameters must be passed by name.
link: The propensity link, one of "logit", "probit", or "cloglog".
convergence_tolerance: The solver convergence tolerance on the tilting moment.
max_iterations: The maximum solver iterations, or NULL for the core default.

Value

An bw_ipt specification, a balance_method.

Details

For each treatment level the propensity p_i = G(x_i' beta) is estimated so that the weighted covariate total matches the target population total. The average treatment effect tilts every level to the whole sample, weighting a unit by the inverse of its modeled propensity. A focal estimand tilts each non-focal level to the focal level, weighting a unit by (1 - p_i) / p_i, and leaves the focal units at weight one. With mean balance and the logit link the tilt solves the same treated-target problem as entropy balancing, so the two methods produce the same average-treatment-effect-on-the-treated weights for a binary exposure.

The weights solve smooth estimating equations regardless of the requested tolerance, which balance() records for the M-estimation variance in ipw().

References

Graham, B. S., Pinto, C. C. de X., and Egel, D. (2012). Inverse probability tilting for moment condition models with missing data. The Review of Economic Studies, 79(3), 1053-1079.

Examples

n <- 200
x1 <- rnorm(n)
x2 <- rnorm(n)
df <- data.frame(
  exposure = rbinom(n, 1, plogis(0.5 * x1 - 0.5 * x2)),
  x1 = x1,
  x2 = x2
)
fit <- balance(df, exposure, c(x1, x2), method = bw_ipt())
#> ℹ Treating `.exposure` as binary
fit
#> 
#> ── Inverse probability tilting ─────────────────────────────────────────────────
#> Exposure: "exposure" (binary)
#> Estimand: "ate"
#> Observations: 200
#> Solver: converged in 3 iterations
#> Constraints: 2 terms (tolerance 0)
#> Largest imbalance: 0.0000 (standardized mean difference)