Raking ratio estimation by iterative proportional fitting

Each pass rescales within one margin, which breaks the previous margin, which is why this iterates rather than solving once. It converges when the margins are consistent (a common total) and no level with a positive target is empty in the sample; both conditions are checked rather than left to diverge silently.

Usage

Raklng(y, weights, margins, tol = 1e-12, max_iter = 200)

Arguments

y

Observed values (used only for the raked estimate).

weights

Starting weights, positive.

margins

List of margins; each is list(labels, targets) where targets is a named numeric vector.

tol

Convergence tolerance on the largest margin discrepancy.

max_iter

Maximum passes.

Value

List with estimate, weights, iterations, max_margin_error, N, n.

Details

Formula: repeat over margins A, B, ...: w_i <- w_i m^A_h / sum_{j in h} w_j for every level h, until every margin matches its target.

References

Deming, W. E. & Stephan, F. F. (1940). On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. Annals of Mathematical Statistics 11(4):427-444. doi:10.1214/aoms/1177731829 .

Examples

y <- c(10, 12, 9, 15, 11, 14)
w <- rep(1, 6)
sex <- c("f", "m", "f", "m", "f", "m"); age <- c("y", "y", "o", "o", "y", "o")
margins <- list(list(labels = sex, targets = c(f = 300, m = 300)),
                list(labels = age, targets = c(y = 250, o = 350)))
r <- Raklng(y, w, margins)
c(r$estimate, r$max_margin_error)
#> [1] 1.186462e+01 4.547474e-13