Description Details Note Author(s) References See Also Examples

This package implements unit-level (Battese et al. 1988) and area-level EBLUP (Fay and Herriot 1979), and GREG (Sarndal 1984) estimators as well as their variance/MSE estimators. It also contains data and a vignette that explain its use. Heteroscedasticity can be considered.

The aim in the analysis of sample surveys is frequently to derive estimates of subpopulation characteristics. Often, the sample available for the subpopulation is, however, too small to allow a reliable estimate. If an auxiliary variable exists that is correlated with the variable of interest, small area estimation (SAE) provides methods to solve the problem (Rao 2003, Rao and Molina 2015).

The purpose of this package is primarily to document the functions used in the publications Breidenbach and Astrup (2012) and Breidenbach et al. (2018). The data used in Breidenbach and Astrup (2012) are provided. A subset of the data used in Breidenbach et al. (2018) is also provided for testing the functions. The vignette further documents the publication Breidenbach et al. (2015).

You might wonder why this package is called JoSAE. Well, first of all, JoSAE sounds good (if pronounced like the female name). The other reason was that the packages SAE and SAE2 already exist (Gomez-Rubio, 2008). They are, however, not available on CRAN and unmaintained (as of July 2011). They also do not seem to implement the variance estimators that we needed. So I just combined SAE with the first part of my name.

All the implemented functions/estimators are described in Rao (2003). This package merely makes the use of the estimators easier for the users that are not keen on programming. Especially the EBLUP variance estimator would require some effort.

Today, there are several well programmed SAE packages available on CRAN that also provide the functions described here. This was not the case when the first version of the package was uploaded. This package is therefore mostly to document the publications mentioned above. With respect to heteroskedasticity, this package also implements functions that, as far as I can see, are not available in other packages (as of May 2018).

Johannes Breidenbach

Maintainer: Johannes Breidenbach <[email protected]>

Battese, G. E., Harter, R. M. & Fuller, W. A. (1988), An error-components model for prediction of county crop areas using survey and satellite data Journal of the American Statistical Association, 83, 28-36

Breidenbach, J. and Astrup, R. (2012), Small area estimation of forest attributes in the Norwegian National Forest Inventory. European Journal of Forest Research, 131:1255-1267.

Breidenbach, J., Ronald E. McRoberts, Astrup, R. (2016), Empirical coverage of model-based variance estimators for remote sensing assisted estimation of stand-level timber volume. Remote Sensing of Environment, 173, 274-281. https://doi.org/10.1016/j.rse.2015.07.026

Breidenbach, J., Rahlf, J., Magnussen, S., Astrup, R. (2018) Unit-level and area-level small area estimation under heteroscedasticity using digital aerial photogrammetry data. Remote Sensing of Environment. In press.

Fay, R. E., Herriot, R. A., 1979. Estimates of income for small places: an application of James- Stein procedures to census data. Journal of the American Statistical Association 74 (366a), 269-277.

Gomez-Rubio (2008), Tutorial on small area estimation, UseR conference 2008, August 12-14, Technische Universitat Dortmund, Germany.

Rao, J.N.K. (2003), Small area estimation. Wiley.

Rao, J. N., Molina, I., (2015). Small area estimation, 2nd Edition. John Wiley & Sons.

Sarndal, C. (1984), Design-consistent versus model-dependent estimation for small domains Journal of the American Statistical Association, JSTOR, 624-631

Schoch, T. (2011), rsae: Robust Small Area Estimation. R package version 0.1-3.

`eblup.mse.f.wrap`

,
`JoSAE.sample.data`

, `JoSAE.domain.data`

,
`sae.al.f`

, `sae.ul.f`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
#mean auxiliary variables for the populations in the domains
data(JoSAE.domain.data)
#data for the sampled elements
data(JoSAE.sample.data)
plot(biomass.ha~mean.canopy.ht,JoSAE.sample.data)
## use the original wrapper function
#lme model
summary(fit.lme <- lme(biomass.ha ~ mean.canopy.ht, data=JoSAE.sample.data
, random=~1|domain.ID))
#domain data need to have the same column names as sample data or vice versa
d.data <- JoSAE.domain.data
names(d.data)[3] <- "mean.canopy.ht"
result <- eblup.mse.f.wrap(domain.data = d.data, lme.obj = fit.lme)
result
##END: use the original wrapper function
## the same with a newer function that can consider heteroskedasticity
res <-
sae.ul.f(samp.data=JoSAE.sample.data,
population.data=d.data,
#assuming homoskedasticity
k.ij=rep(1, nrow(JoSAE.sample.data)),
formula=biomass.ha ~ mean.canopy.ht,
domain.col="domain.ID",
sample.id.col="sample.ID",
neg.sfrac=TRUE)
res$est$est
##END: the same with a newer function that can consider heteroskedasticity
``` |

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