eblup.mse.f.wrap: Functions to calculate the variance of an EBLUP estimate.
In JoSAE: Unit-Level and Area-Level Small Area Estimation

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Functions to calculate the EBLUP MSE (=variance). The wrap function calls all the other functions and calculates EBLUP, GREG, SRS, and Synthetic estimates for domain means as well as the variances of the EBLUP, GREG and SRS estimates.

eblup.mse.f.wrap(domain.data, lme.obj, debug=F, ...)
eblup.mse.f.gamma.i(lme.obj, n.i, ...)
eblup.mse.f.c1(lme.obj, n.i, gamma.i, ...)
eblup.mse.f.c2.ai(lme.obj, n.i, gamma.i, X.i, ...)
eblup.mse.f.c2(gamma.i, X.i, X.bar.i, sum.A.i, ...)
eblup.mse.f.c3.asyvarcovarmat(lme.obj, n.i, ...)
eblup.mse.f.c3(lme.obj, asympt.var.covar, n.i, ...)
eblup.mse.f.c3.star(lme.obj, asympt.var.covar, n.i, mean.resid.i, ...)

`domain.data`	data set with the mean of the auxiliary variables for every domain including the domain ID. Names of the variables must be the same as in the unit-level sample data that were used to fit the lme model.
`lme.obj`	a linear mixed-effects model generated with `lme`
`n.i`	the number of samples within domain i
`gamma.i`	the gamma_i value resulting from the gamma.i method of this function
`X.i`	the design matrix of sampled elements in domain i
`X.bar.i`	mean of the populations elements design matrix in domain i
`sum.A.i`	sum of the domains A_i matrices resulting from `eblup.mse.f.c2.ai`
`asympt.var.covar`	the asymptotic variance-covariance matrix of the mixed-effects model resulting from `eblup.mse.f.c3.asyvarcovarmat`
`mean.resid.i`	the mean residual of the fixed-part of the linear mixed-effects model in domain i (i.e., use `level=0` in `predict.lme`)
`...`	forward attributes to other functions. Not used so far.
`debug`	details are printed if true - Only used by the wrapper function

Most users will probably only use the convenient wrap function. Nonetheless, all components of the EBLUP variance can also be calculated separately.

A compontent of the EBLUP variance (aka mean squared error). Which component depends on the function used.

The wrap function returns a data frame with many entrys for every domain: The domain-level predictor variables obtained from the domain.data, the mean of the predictor variables and response (aka the sample mean or SRS estimate) observed at the samples, the number of samples (n.i.sample), the mean residuals of a lm (fitted using the fixed part of the lme) and the lme (mean.resid.lm, mean.resid.lme), the synthetic (Synth), EBLUP, and GREG estimates of the mean of the variable of interest, the gamma_i value, the variance of the means for the sample and GREG estimates (.var.mean), the components of the EBLUP variance (c1-c3star), the results of the first and the second method (cf. Rao 2003) to derive the EBLUP variance (EBLUP.var.1, EBLUP.var.2), and the standard errors derived from the variances (.se).

Currently, only random intercept mixed-effects models with homogeneous variance structure are supported.

Johannes Breidenbach

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

JoSAE-package for more examples

library(nlme)
data(JoSAE.sample.data)
#fit a lme 
summary(fit.lme <- lme(biomass.ha ~ mean.canopy.ht, data=JoSAE.sample.data
                       , random=~1|domain.ID))
#calculate the first component of the EBLUP variance for a domain with 5 samples
eblup.mse.f.c1(fit.lme, 5, 0.2)