fitEB: fitSTEBLUP
In wahani/SAE: Small Area Estimation

Wrapper function for the estimation of a FH model. Uses the function fitFH provided by Sample Deliverable 22: Software on Small Area Estimation

fitEB(formula, dat, beta, sigma, rho,
  sigmaSamplingError = seSigmaClosure(nDomains, nTime)(),
  nDomains = getNDomains(dat), nTime = getNTime(dat),
  w0 = w0Matrix(nDomains), w = w0/rowSums(w0), tol = 0.001,
  method = "Nelder-Mead", maxIter = 500)

`formula`	formula for the fixed effects part
`dat`	data with dependent and independent variable as they are used in formula. The data should contain a variable `Domain` and `Time` indicating the domain and time period for each observation respectively - only the last time period will be used for estimation and prediction.
`beta,`	sigma, rho start values for the parameters - not needed in the call to `fitFH`
`sigmaSamplingError`	True variances for the sampling errors
`nDomains`	the number of domains. Will be determined by default, see `dat` - not needed in the call to `fitFH`
`nTime`	the number of time periods. Will be determined by default, see `dat` - not needed in the call to `fitFH`
`w0`	proximity matrix - not needed in the call to `fitFH`
`w`	at the moment row-standardized proximity matrix - not needed in the call to `fitFH`
`tol`	numerical tolerance for algorithm - not needed in the call to `fitFH`
`method`	method used by the function `optim` - not needed in the call to `fitFH`
`maxIter`	maximal number of iterations

require(spatioTemporalData); require(SAE)
set.seed(3)
setup <- simSetupMarhuenda(nDomains=30, nTime=5, sarCorr=0.5, arCorr=0.5, n = 200)
output <- simRunMarhuenda(setup)
dat <- slot(output[[1]], "data")[[1]]
result <- fitEB(y~x, dat, c(0,1), c(1,1), c(0.5,0.5))
#summary(result)