Small Area Estimation - Sampling Spatial Units for Agricultural Surveys - page 274

If the aim is to calculate the direct HT estimates for all the SAs, we can use the
following code.

> domdir < - svyby(~yobs,~coddom,dsrs,svymean)
> domdir

coddom yobs se

11 11 80.12641 4.8138426

12 12 93.52410 3.9684518

13 13 74.28390 5.6532726

21 21 101.37026 4.5704614

22 22 119.01017 0.8044394

23 23 96.89364 4.2063243

31 31 78.69029 3.9254892

32 32 98.91292 5.6468604

33 33 83.37624 4.5737139

The first argument in svyby specifies the variables to be analyzed (i.e.,
~yobs), the second denotes the grouping variables that define the subpopulations
(i.e., ~coddom), the third is a svydesign object that identifies the sampling
design (i.e., dsrs), and the fourth identifies the analysis to be performed on each
subpopulation, in this case a sample mean (i.e., svymean). The output provides the
estimates and standard deviations (i.e., column se) for each SA.
The HT direct estimates for all the SAs can be also obtained with the sae
package using the following commands.

> dtab < - table(framepop$coddom)
> dsize < - as.data.frame(cbind(as.numeric(names(dtab)),dtab))
> colnames(dsize) < - c("coddom","Freq")
> domdirsae < - direct(y ¼ yobs,dom ¼ coddom, domsize ¼ dsize, data ¼ framesrs,
+ replace ¼ F)

> domdirsae

Domain SampSize Direct SD CV

1 11 14 80.12641 4.9187668 6.138758

9 12 9 93.52410 4.2399097 4.533494

8 13 13 74.28390 5.7951789 7.801393

2 21 8 101.37026 4.9310622 4.864407

3 22 11 119.01017 0.8398941 0.705733

4 23 12 96.89364 4.3224972 4.461074

7 31 11 78.69029 4.0855991 5.191999

6 32 9 98.91292 6.0331281 6.099434

5 33 13 83.37624 4.7047441 5.642788

Note that the standard deviations of the direct estimates obtained with sae are
different from those calculated using survey. As stated in the help files of sae,