PracTools (version 1.7.5)

deffCR: Chen-Rust design effect

Description

Chen-Rust design effect for an estimated mean from a stratified, clustered, two-stage sample

Usage

deffCR(w, strvar=NULL, clvar=NULL, clnest=NULL, Wh=NULL, y, stages)

Value

A list with components:

strata components

Matrix with number of sample first-stage units, intracluster correlation (rhoh), coefficient of variation of the weights (cv2wh), and deff's due to weighting (deff.w), clustering (deff.c), and stratification (deff.s) for each stratum. When strvar or clvar are NULL appropriate subsets of these are output.

overall deff

Design effect for full sample accounting for weighting, clustering, and stratification. This is computed from Deff* in Chen-Rust (2017, top of p.117) and may differ from a directly computed deff based on the ratio of the complex sample variance to the simple random sample from, e.g., the survey package.

Arguments

w

vector of weights for a sample; weights should be scaled for estimating population totals

strvar

vector of stratum identifiers; equal in length to that of w.

clvar

vector of cluster identifiers; equal in length to that of w.

clnest

Are cluster IDs numbered within strata (TRUE or FALSE)? If TRUE, cluster IDs can be restarted within strata, e.g., 1,2,3,1,2,3,...

Wh

vector of the proportions of elements that are in each stratum; length is number of strata.

y

vector of the sample values of an analysis variable

stages

Number of stages used in sampling in each stratum. stages must be in the same order as the sorted, unique values of strvar and must be a combination of 1s and 2s, e.g. c(1,2,2,1) if there are four strata.

Author

Richard Valliant, Jill A. Dever, Frauke Kreuter

Details

The Chen-Rust deff for an estimated mean accounts for stratification, clustering, and unequal weights, but does not account for the use of any auxiliary data in the estimator of a mean. The formula is based on a superpopulation model in which units have a common mean within each stratum; units are correlated within clusters but units in different clusters are uncorrelated. The Chen-Rust deff returned here is appropriate for stratified, one-stage or two-stage sampling. Designs may have a combination of one-stage sampling in some strata and two-stage sampling in others. Separate deff's are produced for weighting, clustering, and stratification within each stratum. These cannot be added across strata unless the stratum values of the coefficient of variation of the weights, the sample size of clusters, and the intracluster correlation of y are equal across all strata (see Chen and Rust 2017, p.117).

The weights in w should be scaled for estimating population totals. If the weights sum to the sample size or less in any stratum or overall, an error will result. This can occur if normalized weights are used. All sampling within a stratum must have the same number of stages. In particular, all sampling must be either 2-stage cluster sampling or single-stage sampling. If the vector Wh is not supplied for a stratified sample, it will be estimated based on w.

References

Chen, S. and Rust, K. (2017). An Extension of Kish's Formula for Design Effects to Two- and Three-Stage Designs with Stratification. Journal of Survey Statistics and Methodology, 5(2), 111-130.

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 14). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

deff, deffH, deffK, deffS

Examples

require(PracTools)
require(sampling)
require(reshape)
data(MDarea.popA)

Ni <- table(MDarea.popA$TRACT)
m <- 20
probi <- m*Ni / sum(Ni)
# select sample of clusters
set.seed(-780087528)
sam <- sampling::cluster(data=MDarea.popA, clustername="TRACT", size=m,
                         method="systematic",
                         pik=probi, description=TRUE)
# extract data for the sample clusters
samclus <- getdata(MDarea.popA, sam)
samclus <- rename(samclus, c("Prob" = "pi1"))
# treat sample clusters as strata and select srswor from each
nbar <- 8
s <- sampling::strata(data = as.data.frame(samclus), stratanames = "TRACT",
                      size = rep(nbar,m), method="srswor")
# extracts the observed data
samdat <- getdata(samclus,s)
samdat <- rename(samdat, c("Prob" = "pi2"))
  # add artificial stratum ID
H <- 4
nh <- m * nbar / H
strat1 <- NULL
for (h in 1:H){
  strat1 <- c(strat1, rep(h,nh))
}
wt <- 1/(samdat$pi1*samdat$pi2) * runif(m*nbar)
samdat <- cbind(subset(samdat, select = -c(Stratum)), strat1, wt)

  # 4 strata, SRS in each
deffCR(w = samdat$wt, strvar = samdat$strat1, clvar = NULL,
       Wh=NULL, y=samdat$y2, clnest = NULL, stages = c(1,1,1,1))

  # 4 strata + clusters; 2 stages in 4 strata
deffCR(w = samdat$wt, strvar = samdat$strat1, clvar = samdat$TRACT,
       Wh=NULL, y=samdat$y2, clnest = FALSE, stages = c(2,2,2,2))

  # 4 strata, SRS in strata 1 & 4, 2-stage in strata 2, 3
deffCR(w = samdat$wt, strvar = samdat$strat1, 
       clvar = c(1:40, rep(1,20), rep(2,20), rep(1,20), rep(2,20), 1:40),
       Wh=NULL, y=samdat$y2, clnest = TRUE, stages = c(1,2,2,1))