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 true shapes of the trend and spread terms. |
d |
a numeric vector of length two giving the assumed shapes of the trend and spread terms. |
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 (πps–reg, STSI–reg, STSI–HT, πps–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 πps–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 πps–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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