Description Usage Arguments Details Value References See Also Examples

Compute the expected variance of five sampling strategies.

1 2 |

`b` |
a numeric vector of length two giving the |

`d` |
a numeric vector of length two giving the |

`x` |
a positive numeric vector giving the values of the auxiliary variable. |

`n` |
a positive integer indicating the desired sample size. |

`H` |
a positive integer giving the
desired number of strata/poststrata. Ignored if |

`Rxy` |
a number giving the correlation between the auxiliary variable and the study variable. |

`stratum1` |
a list giving stratum and sample sizes per stratum (see ‘Details’). |

`stratum2` |
a list giving stratum and sample sizes per stratum (see ‘Details’). |

`st` |
a numeric vector indicating the strategies for which the expected variance is to be calculated (see ‘Details’). |

`short` |
logical. If |

The expected variance of a sample of size `n`

is computed for
five sampling strategies (*π*ps–reg, STSI–reg, STSI–HT, *π*ps–pos and STSI–pos).

The strategies are defined assuming that the underlying superpopulation model is of the form

*Y_k = δ_0 + δ_1 x_k^δ_2 + ε_k*

with *Eε_k = 0*, *Vε_k = δ_3^2 x_k^2δ_4* and *Cov(ε_k , ε_l) = 0*. But the true generating model is of the form

*Y_k = β_0 + β_1 x_k^β_2 + ε_k*

with *Eε_k = 0*, *Vε_k = β_3^2 x_k^2β_4* and *Cov(ε_k , ε_l) = 0*.

The parameters *β_2* and *β_4* are given by `b`

. The parameters *δ_2* and *δ_4* are given by `d`

.

`stratum1`

and `stratum2`

are lists with two components (each with length `length(x)`

): `stratum`

indicates the stratum to which each element belongs and `nh`

indicates the sample sizes to be selected in each stratum. They can be created via `optiallo`

. `stratum1`

gives the stratification for STSI–HT and the poststrata for *π*ps–pos and STSI–pos; whereas `stratum2`

gives the stratification for STSI–reg and STSI–pos. If `NULL`

, `optiallo`

is used for defining `H`

strata/poststrata.

`st`

indicates which variances to be calculated. If `1 in st`

, the expected variance of *π*ps–reg is calculated. If `2 in st`

, the expected variance of STSI–reg is calculated, and so on.

If `short=FALSE`

a vector of length five is returned giving the expected variance of the strategies given in `st`

. `NA`

is returned for those strategies not given in `st`

. If `short=TRUE`

, the `NA`

s are omitted.

Bueno, E. (2018). *A Comparison of Stratified Simple Random Sampling and Probability Proportional-to-size Sampling.* Research Report, Department of Statistics, Stockholm University 2018:6. http://gauss.stat.su.se/rr/RR2018_6.pdf.

`optiallo`

for how to stratify an auxiliary variable and allocate the sample size; `desvar`

for calculating the variance of the five strategies.

1 2 3 4 5 6 7 8 9 | ```
x<- 1 + sort( rgamma(5000, shape=4/9, scale=108) )
expvar(b=c(1,1),d=c(1,1),x,n=500,H=6,Rxy=0.9)
expvar(b=c(1,1),d=c(1,1),x,n=500,H=6,Rxy=0.9,st=1:3)
expvar(b=c(1,1),d=c(1,1),x,n=500,H=6,Rxy=0.9,st=1:3,short=TRUE)
st1<- optiallo(n=500,x,H=6)
post1<- optiallo(n=500,x^1.5,H=10)
expvar(b=c(1,1),d=c(1,1),x,n=500,H=6,Rxy=0.9,
stratum1=post1,stratum2=st1)
``` |

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