weighted_energy_stats {independenceWeights}

Calculation of weighted energy statistics for weighted dependence

Description

Calculates weighted energy statistics used to quantify weighted dependence

Usage

weighted_energy_stats(A, X, weights, dimension_adj = TRUE)

Arguments

A

treatment vector indicating values of the treatment/exposure variable.

X

matrix of covariates with number of rows equal to the length of weights and each column is a covariate

weights

a vector of sample weights

dimension_adj

logical scalar. Whether or not to add adjustment to energy distance terms that account for the dimensionality of x. Defaults to TRUE.

Value

a list with the following components

D_w

The value of the weighted dependence distance of Huling, et al. (2021) using the optimal estimated weights. This is the weighted dependence statistic without the ridge penalty on the weights.

distcov_unweighted

The unweighted distance covariance term. This is the standard distance covariance of Szekely et al (2007). This term is always equal to D_unweighted.

distcov_weighted

The weighted distance covariance term. This term itself does not directly measure weighted dependence but is a critical component of it.

energy_A

The weighted energy distance between A and its weighted version

energy_X

The weighted energy distance between X and its weighted version

ess

The estimated effective sample size of the weights using Kish's effective sample size formula.

An object of class "weighted_energy_terms".

D_w

the value of the DCOW measure

distcov_unweighted

the unweighted distance covariance between treatment and covariates

distcov_weighted

the weighted distance covariance between treatment and covariates

energy_A

the (energy) distance between the treatment distribution and the weighted treatment distribution. Smaller values mean the marginal distribution of the treatment is preserved after weighting

energy_x

the (energy) distance between the covariate distribution and the weighted covariate distribution. Smaller values mean the marginal distribution of the covariates is preserved after weighting

ess

the expected sample size after weighting. Kish's approximation is used

References

Szekely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing dependence by correlation of distances. Annals of Statistics 35(6) 2769-2794 doi: 10.1214/009053607000000505

Huling, J. D., Greifer, N., & Chen, G. (2021). Independence weights for causal inference with continuous exposures. arXiv preprint arXiv:2107.07086. https://arxiv.org/abs/2107.07086

Examples

simdat <- simulate_confounded_data(seed = 999, nobs = 100)

str(simdat$data)

A <- simdat$data$A
X <- as.matrix(simdat$data[c("Z1", "Z2", "Z3", "Z4", "Z5")])

wts <- runif(length(A))

weighted_energy_stats(A, X, wts)