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Computes the effective sample size (ESS) of a weighted sample, which represents the size of an unweighted sample with approximately the same amount of precision as the weighted sample under consideration.

The ESS is calculated as \((\sum w)^2/\sum w^2\).

Usage

ESS(w)

Arguments

w

a vector of weights

References

McCaffrey, D. F., Ridgeway, G., & Morral, A. R. (2004). Propensity Score Estimation With Boosted Regression for Evaluating Causal Effects in Observational Studies. Psychological Methods, 9(4), 403–425. doi:10.1037/1082-989X.9.4.403

Shook‐Sa, B. E., & Hudgens, M. G. (2020). Power and sample size for observational studies of point exposure effects. Biometrics, biom.13405. doi:10.1111/biom.13405

Examples


library("cobalt")
#>  cobalt (Version 4.5.5, Build Date: 2024-04-02)
data("lalonde", package = "cobalt")

#Balancing covariates between treatment groups (binary)
(W1 <- weightit(treat ~ age + educ + married +
                  nodegree + re74, data = lalonde,
                method = "glm", estimand = "ATE"))
#> A weightit object
#>  - method: "glm" (propensity score weighting with GLM)
#>  - number of obs.: 614
#>  - sampling weights: none
#>  - treatment: 2-category
#>  - estimand: ATE
#>  - covariates: age, educ, married, nodegree, re74
summary(W1)
#>                   Summary of weights
#> 
#> - Weight ranges:
#> 
#>            Min                                   Max
#> treated 1.5560  |--------------------------| 73.3315
#> control 1.0222 ||                             3.0438
#> 
#> - Units with the 5 most extreme weights by group:
#>                                                 
#>              124     184     172     181     182
#>  treated 11.2281 11.3437 12.0848 26.1775 73.3315
#>              411     595     269     409     296
#>  control  2.3303  2.4365  2.5005  2.6369  3.0438
#> 
#> - Weight statistics:
#> 
#>         Coef of Var   MAD Entropy # Zeros
#> treated       1.609 0.555   0.403       0
#> control       0.247 0.211   0.029       0
#> 
#> - Effective Sample Sizes:
#> 
#>            Control Treated
#> Unweighted  429.    185.  
#> Weighted    404.35   51.73
ESS(W1$weights[W1$treat == 0])
#> [1] 404.3484
ESS(W1$weights[W1$treat == 1])
#> [1] 51.73462