Energy balancing

bw_energy() specifies energy balancing for balance(). The weights minimize the energy distance between the reweighted exposure groups and a target sample, subject to a simplex-type constraint set, so the reweighting improves multivariate covariate balance without positing a propensity model. Energy balancing supports binary, categorical, and continuous exposures.

Usage

bw_energy(
  ...,
  distance = c("scaled_euclidean", "mahalanobis", "euclidean"),
  improved = TRUE,
  weight_penalty = 1e-04,
  min_weight = 1e-08,
  distribution_moments = NULL,
  dimension_adjustment = TRUE,
  convergence_tolerance = NULL,
  max_iterations = NULL
)

Arguments

...

Reserved for future extensions; must be empty. Tuning parameters must be passed by name.

distance

The covariate distance definition the energy objective is built on, one of "scaled_euclidean" (each covariate divided by its standard deviation), "mahalanobis", or "euclidean".

improved

Whether to add the between-group energy distance of the improved variant for the average treatment effect with a discrete exposure.

weight_penalty

The L2 penalty on the weights, which stabilizes the quadratic program.

min_weight

The smallest permitted weight. The reported weights average one within each exposure group, so a floor approaching one leaves almost no room above it: the weight spread shrinks in proportion to the headroom 1 - min_weight, and the fit degenerates smoothly into uniform weights and reports the balance uniform weights achieve. Nothing warns at that boundary, because the problem stays feasible and the solution is a real one. bw_sbw(), whose tolerances are hard constraints rather than an objective, refuses the same floor as infeasible instead.

distribution_moments

For a continuous exposure, the number of exposure and covariate marginal moments held equal to the sample under the base measure, or NULL for the constraint moments. Raised automatically when smaller than the constraint moments. Energy balancing carries no base weights, so the base measure is the sampling weights, and without them the marginals are held equal to the unweighted sample.

dimension_adjustment

For a continuous exposure, whether to weight the covariate energy distance by the covariate dimensionality adjustment.

convergence_tolerance

The quadratic-program solver tolerance, or NULL for the core default.

max_iterations

The maximum solver iterations, or NULL for the core default.

Value

An bw_energy specification, a balance_method.

Details

For a binary or categorical exposure the objective is the sum of each group's energy distance to the target sample. The improved variant for the average treatment effect adds the between-group energy distance, which balances the groups against one another as well as against the sample. A focal estimand reweights the non-focal groups toward the focal group, whose units keep their base weight. The energy distance is built from a pairwise covariate distance matrix; distance selects how that matrix is formed.

For a continuous exposure the objective is the weighted distance covariance between the exposure and the covariates, following Huling, Greifer, and Chen, plus the marginal energy distances of the weighted exposure and covariate distributions. distribution_moments sets how many exposure and covariate marginal moments are held equal to the sample under the base measure, and dimension_adjustment reweights the covariate energy distance by the covariate dimensionality.

Energy balancing belongs to the quadratic-program family, which has no estimating equations, so a fit produces no estimating-equations container and the tolerance in balance_terms() relaxes any added moment constraints rather than selecting an inexact solver. A tolerance supplied without moment constraints has nothing to relax, so it is warned and ignored.

References

Huling, J. D. and Mak, S. (2024). Energy balancing of covariate distributions. Journal of Causal Inference, 12(1), 20220029.

Huling, J. D., Greifer, N., and Chen, G. (2024). Independence weights for causal inference with continuous treatments. Journal of the American Statistical Association, 119(546), 1657-1670.

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_energy())
#> ℹ Treating `.exposure` as binary
fit
#> 
#> ── Energy balancing ────────────────────────────────────────────────────────────
#> Exposure: "exposure" (binary)
#> Estimand: "ate"
#> Observations: 200
#> Solver: converged in 75 iterations
#> Constraints: 2 terms (tolerance 0)
#> Largest imbalance: 0.0058 (standardized mean difference)