sae.ul.f_all_UL: Unit-level small area estimation under heteroscedasticity.
In JoSAE: Unit-Level and Area-Level Small Area Estimation

Description Usage Arguments Details Value Author(s) References Examples

The only function that should be used is sae.ul.f which wraps the data preparation (ul.data.prep.f), parameter estimation (ul.reml.f), and EBLUP and MSE estimation (ul.est.f) functions. The other functions are helpers that do not need to be called by the user directly.

sae.ul.f(...)

ul.data.prep.f(k.ij, samp.data, population.data, formula, domain.col,
sample.id.col, neg.sfrac, pop.r, sum.i.k.ij.sq.r, N.i, ...)

ul.reml.f(samp.data, formula, samp.agg.X.pop, y.name, X.names, ...)

ul.est.f(samp.data, samp.agg.X.pop, X.names, y.name, beta.hat,
cov.beta.hat, sig.sq.e, sig.sq.v, V.bar.ee, V.bar.vv, V.bar.ve,
neg.sfrac, resid = F, ...)

`samp.data`	Data frame of unit-level sample data of the response and explanatory variables. Transformations of x have to be calculated before hand, not using formula.
`k.ij`	Vector of the same length and corresponding to `samp.data` containing the `k_ij` values for modeling heteroscedasticity. A vector of 1's if heteroscedasticity is not considered. `k_ij` is squared and used as the input to the `varFix` variance function in `lme`.
`population.data`	Data frame of domain-level means of the explanatory variables. Names have to match to sample data.
`formula`	The fixed effects formula to be used in the mixed model using `lme`.
`domain.col`	Character string identifying the column name in `sample.data` and `population.data` containing unique domain IDs.
`sample.id.col`	Character string identifying the column name in `sample.data` containing unique sample IDs.
`neg.sfrac`	Boolean. Are sampling fractions negligible?
`pop.r`	Only required if `neg.sfrac` is FALSE. Same as `population.data` but calculated with the sample elements removed.
`sum.i.k.ij.sq.r`	Only required if `neg.sfrac` is FALSE. Same as the values in the `population.k.column` but calculated with the sample elements removed.
`N.i`	Only required if `neg.sfrac` is FALSE. Number of elements within domain i.
`samp.agg.X.pop`	Data frame containing the aggregated sample data and domain-level explanatory variables.
`y.name`	Character string identifying the column name of the response.
`X.names`	Vector of character strings identifying the column names of the explanatory variables.
`beta.hat`	Vector of estimated fixed effects.
`cov.beta.hat`	Covariance matrix of fixed effects.
`sig.sq.e`	Residual variance.
`sig.sq.v`	Random effect variance.
`V.bar.ee`	Assymptotic variance of the residual variance.
`V.bar.vv`	Assymptotic variance of the random effect variance.
`V.bar.ve`	Assymptotic covariance of the residual and random effect variance.
`resid`	Boolean. Should residuals be returned?
`...`	Parameters forwarded to other functions.

These functions can also be used for eblups without heteroskedasticity as the the older functions around eblup.mse.f.wrap.

`est`	List of point estimates and standard errors based on different estimators. `est`: Point estimates of EBLUP, SRS, GREG, Survey regression (svreg), and EBLUP synthetic estimators. Also contains random effects. `se`: Standard errors. EBLUP global was used in the reference publication. `resids`: Different forms of raw and transformed residuals.
`var.pars`	List of estimated variance parameters. Among others the lme object fitted to the data. See list of arguments above.
`data`	List of data frames in the format required by the other functions.

Johannes Breidenbach

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

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

#eblup under homoskedasticity
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)

#eblup under heteroskedasticity
res <-
    sae.ul.f(samp.data=ulal.sub.samp.dat,
             population.data=ulal.sub.dom.dat,
             k.ij=ulal.sub.samp.dat[,"k.ij.em.0.48"],
             formula=w.VMPRHA ~ elev.mean + elev.mean.sq,
             domain.col="stand.ID",
             sample.id.col="plot.ID",
             neg.sfrac=TRUE)