IPW estimate with a replicate-weight (jackknife) variance

The point estimate is the Hajek weighted difference in means between treated and control units; its variance comes from the replicate weights supplied with the survey, which is the design-based route when the sampling design is not recoverable from the microdata. The scale factor is exposed so JKn and BRR schemes (factor 1/B) can be used in place of the JK1 default.

Usage

Ipferd(y, D, w, replicate_weights, scale = NULL)

Arguments

y: Outcome vector.
D: Treatment indicator, 0 or 1.
w: Full-sample analysis weights.
replicate_weights: n by B matrix of replicate weights.
scale: Multiplier on the sum of squared deviations; NULL uses the JK1 value (B - 1)/B.

Value

List with estimate, se, variance, scale, replicate_estimates, rep_mean, n_replicates, n, method.

Details

Formula: v(theta) = ((B - 1)/B) sum_b (theta_b - theta)^2.

References

Rust and Rao (1996), Variance estimation for complex surveys using replication techniques, Statistical Methods in Medical Research 5(3):283-310. doi:10.1177/096228029600500305 Lumley (2010), Complex Surveys, Wiley, doi:10.1002/9780470580066 ; Lumley and Scott (2017), Statistical Science 32(2):265-278. doi:10.1214/16-STS605

Examples

set.seed(1)
Ipferd(y = rnorm(20), D = rbinom(20, 1, 0.5), w = runif(20, 1, 2),
       replicate_weights = matrix(runif(200, 0.5, 1.5), 20, 10))
#> $estimate
#> [1] -0.02768028
#> 
#> $se
#> [1] 0.3931372
#> 
#> $variance
#> [1] 0.1545568
#> 
#> $scale
#> [1] 0.9
#> 
#> $replicate_estimates
#>  [1]  0.19822891  0.04445269 -0.06670156 -0.10339738  0.14400747  0.09255423
#>  [7]  0.10514147  0.16051802 -0.05526457  0.07470042
#> 
#> $rep_mean
#> [1] 0.05942397
#> 
#> $n_replicates
#> [1] 10
#> 
#> $n
#> [1] 20
#> 
#> $method
#> [1] "Hajek weighted difference; v = ((B-1)/B) sum_b (theta_b - theta)^2, Rust & Rao (1996) JK1"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"