sae.al.f {JoSAE}

Area-level small area estimation under heteroscedasticity or homoscedasticity.

Description

Area-level small area estimation, possibly under heteroscedasticity. Assumes SRS within domains.

Usage

sae.al.f(domain.id, n.i, psi.i, formula, data, b.i, type = "RE", verbose
= F, iter = 100, a.conv = 0.001,...) 

Arguments

domain.id

Vector of unique domain IDs corresponding to data.

n.i

Vector of number of samples within each domain i, corresponding to data.

psi.i

Vector of variances of the direct estimator within each domain i, corresponding to data.

formula

Formula for fixed effects.

data

Domain-level data.

b.i

Parameter for modeling heteroscedasticity.

type

Method for estimating variance parameters. Currently, only option is "RE" for REML.

verbose

Boolean. Should more info be printed?

iter

Max number of iterations. Default is 100.

a.conv

Threshold for accepting convergency. Default is 0.001

...

Parameters forwarded to other functions.

Details

SRS (simple random sampling) is assumed within each domain. If the direct estimator is not based on SRS, RV components of the results do not make sense.

Value

results

Area-level estimates and associated standard errors (SE). FH Fay-Harriot estimate (the standard area-level estimator), RV Rivest-Vandal estimate, considering uncertainty in variance parameters. bias.sig.sq.v Bias in random effect variance. synth Synthetic estimate. trans.resid.v.i Transformed residuals. The other parameters are details and are named as in the reference.

beta.hat

Estimated fixed-effects parameters.

des.mat

Design matrix.

Other list elements have descriptive names.

Author(s)

Johannes Breidenbach

References

Breidenbach et al. (2018) Unit-level and area-level small area estimation under heteroscedasticity using digital aerial photogrammetry data. Remote Sensing of Environment.

Examples

library(nlme)
#sample data
data(ulal.sub.samp.dat)
#domain means of x
data(ulal.sub.dom.dat)

#The easiest way of getting the data into the right format
#is to fit a unit-level model first.
res <-
    sae.ul.f(samp.data=ulal.sub.samp.dat,
             population.data=ulal.sub.dom.dat,
             k.ij=ulal.sub.samp.dat[,"k.ij.one"],
             formula=w.VMPRHA ~ elev.mean + elev.mean.sq,
             domain.col="stand.ID",
             sample.id.col="plot.ID",
             neg.sfrac=TRUE)

#data for AL
dat.al <- merge(res$data$samp.agg.X.pop[,c("domain.id","n.i","w.VMPRHA.ybar.i","elev.mean.X.pop")],
                res$est$se[,c("domain.id","se.srs")])

#area-level SAE under homoscedasticity
res <- sae.al.f(
    domain.id=dat.al$domain.id , n.i=dat.al$n.i , psi.i=dat.al$se.srs^2
    , formula=w.VMPRHA.ybar.i ~ elev.mean.X.pop , data=dat.al
    , b.i=rep(1, nrow(dat.al))
    , type="RE")

#area-level SAE heteroskedasticity
bi.par <- 0.39#select b.i parameter
#helper function
range01 <- function(x, ...){(x - min(x, ...)) /
                                (max(x, ...) - min(x, ...))}
res <- sae.al.f(
    domain.id=dat.al$domain.id , n.i=dat.al$n.i , psi.i=dat.al$se.srs^2
    , formula=w.VMPRHA.ybar.i ~ elev.mean.X.pop, data=dat.al
    , b.i=range01(dat.al$elev.mean.X.pop)+bi.par
    , type="RE")