Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 117

> # Overton approximation
> dpps < - svydesign(id ¼ ~1,data ¼ framepps,
+ fpc ¼ ~framepps$probinc,pps ¼ "overton")
> epps < - svytotal(~yobs+as.factor(q1obs),dpps)
> epps

total SE
yobs 86151.05 19275.47
as.factor(q1obs)1 291.00 142.78
as.factor(q1obs)2 345.40 187.78
as.factor(q1obs)3 246.13 77.01
> # without replacement approximation
> dpps < - svydesign(id ¼ ~1,data ¼ framepps,probs ¼ ~framepps$probinc)
> epps < - svytotal(~yobs+as.factor(q1obs),dpps)
> epps

total SE

yobs 86151.05 19236.04

as.factor(q1obs)1 291.00 143.52

as.factor(q1obs)2 345.40 188.38

as.factor(q1obs)3 246.13 78.02

The approximations are very similar to each other, but what is interesting is that
the results may be even worse than those obtained with SRS. This demonstrates that
a proportional to size scheme is not necessarily better than a simple scheme, if the
auxiliary variable is not highly correlated with the variable of interest, and it could
introduce a noticeable loss in efficiency. If we use a covariate with a correlation
higher than 0.9, we expect to reduce the uncertainty of the estimator.

> set.seed(200694)
> ypps < - (yobs + rnorm(N)*10)
> cor(yobs,ypps)
[1] 0.9103131

> probinc < - inclusionprobabilities(ypps,n)
> framepop < - cbind(framepop[,1:6],probinc)
> set.seed(200694)
> pps < - UPtille(probinc)
> pps < - round(pps)
> framepps < - framepop[pps ¼¼ 1,]

> # without replacement approximation
> dpps < - svydesign(id ¼ ~1,data ¼ framepps,probs ¼ ~framepps$probinc)
> epps < - svytotal(~yobs+as.factor(q1obs),dpps,deff ¼ T)
> epps