deffH {PracTools}

Henry design effect for pps sampling and GREG estimation of totals

Description

Compute the Henry design effect for single-stage samples when a general regression estimator is used for a total.

Usage

deffH(w, y, x)

Arguments

w

vector of inverses of selection probabilities for a sample

y

vector of the sample values of an analysis variable

x

matrix of covariates used to construct a GREG estimator of the total of y. This matrix does not include the intercept.

Details

The Henry design effect is the ratio of the variance of the general regression (GREG) estimator of a total of y to the variance of the estimated total in srswr. Calculations for the Henry deff are done as if the sample is selected in a single-stage and with replacement. Varying selection probabilities can be used. The model for the GREG is assumed to be y = \alpha + \beta x + \epsilon, i.e., the model has an intercept.

Value

numeric design effect

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Henry, K.A., and Valliant, R. (2015). A Design Effect Measure for Calibration Weighting in Single-stage Samples. Survey Methodology, 41, 315-331.

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, deffCR, deffK, deffS

Examples

set.seed(-500398777)
    # generate population using HMT function
pop.dat <- as.data.frame(HMT())
mos <- pop.dat$x
pop.dat$prbs.1d <- mos / sum(mos)
    # select pps sample
require(sampling)
n <- 80
pk <- n * pop.dat$prbs.1d
sam <- UPrandomsystematic(pk)
sam <- sam==1
sam.dat <- pop.dat[sam, ]
dsgn.wts <- 1/pk[sam]
deffH(w=dsgn.wts, y=sam.dat$y, x=sam.dat$x)