# rake: Raking of replicate weight design In survey: Analysis of Complex Survey Samples

## Description

Raking uses iterative post-stratification to match marginal distributions of a survey sample to known population margins.

## Usage

 ```1 2``` ```rake(design, sample.margins, population.margins, control = list(maxit = 10, epsilon = 1, verbose=FALSE), compress=NULL) ```

## Arguments

 `design` A survey object `sample.margins` list of formulas or data frames describing sample margins, which must not contain missing values `population.margins` list of tables or data frames describing corresponding population margins `control` `maxit` controls the number of iterations. Convergence is declared if the maximum change in a table entry is less than `epsilon`. If `epsilon<1` it is taken to be a fraction of the total sampling weight. `compress` If `design` has replicate weights, attempt to compress the new replicate weight matrix? When `NULL`, will attempt to compress if the original weight matrix was compressed

## Details

The `sample.margins` should be in a format suitable for `postStratify`.

Raking (aka iterative proportional fitting) is known to converge for any table without zeros, and for any table with zeros for which there is a joint distribution with the given margins and the same pattern of zeros. The ‘margins’ need not be one-dimensional.

The algorithm works by repeated calls to `postStratify` (iterative proportional fitting), which is efficient for large multiway tables. For small tables `calibrate` will be faster, and also allows raking to population totals for continuous variables, and raking with bounded weights.

## Value

A raked survey design.

`postStratify`, `compressWeights`
`calibrate` for other ways to use auxiliary information.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58``` ```data(api) dclus1 <- svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc) rclus1 <- as.svrepdesign(dclus1) svymean(~api00, rclus1) svytotal(~enroll, rclus1) ## population marginal totals for each stratum pop.types <- data.frame(stype=c("E","H","M"), Freq=c(4421,755,1018)) pop.schwide <- data.frame(sch.wide=c("No","Yes"), Freq=c(1072,5122)) rclus1r <- rake(rclus1, list(~stype,~sch.wide), list(pop.types, pop.schwide)) svymean(~api00, rclus1r) svytotal(~enroll, rclus1r) ## marginal totals correspond to population xtabs(~stype, apipop) svytable(~stype, rclus1r, round=TRUE) xtabs(~sch.wide, apipop) svytable(~sch.wide, rclus1r, round=TRUE) ## joint totals don't correspond xtabs(~stype+sch.wide, apipop) svytable(~stype+sch.wide, rclus1r, round=TRUE) ## Do it for a design without replicate weights dclus1r<-rake(dclus1, list(~stype,~sch.wide), list(pop.types, pop.schwide)) svymean(~api00, dclus1r) svytotal(~enroll, dclus1r) ## compare to raking with calibrate() dclus1gr<-calibrate(dclus1, ~stype+sch.wide, pop=c(6194, 755,1018,5122), calfun="raking") svymean(~stype+api00, dclus1r) svymean(~stype+api00, dclus1gr) ## compare to joint post-stratification ## (only possible if joint population table is known) ## pop.table <- xtabs(~stype+sch.wide,apipop) rclus1ps <- postStratify(rclus1, ~stype+sch.wide, pop.table) svytable(~stype+sch.wide, rclus1ps, round=TRUE) svymean(~api00, rclus1ps) svytotal(~enroll, rclus1ps) ## Example of raking with partial joint distributions pop.imp<-data.frame(comp.imp=c("No","Yes"),Freq=c(1712,4482)) dclus1r2<-rake(dclus1, list(~stype+sch.wide, ~comp.imp), list(pop.table, pop.imp)) svymean(~api00, dclus1r2) ## compare to calibrate() syntax with tables dclus1r2<-calibrate(dclus1, formula=list(~stype+sch.wide, ~comp.imp), population=list(pop.table, pop.imp),calfun="raking") svymean(~api00, dclus1r2) ```