# deffH: Henry design effect for _pps_ sampling and GREG estimation of... In PracTools: Tools for Designing and Weighting Survey Samples

 deffH R Documentation

## 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 = α + β x + ε, 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.

`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)
```

PracTools documentation built on Aug. 17, 2022, 5:06 p.m.