predictFit: Predict Method for (Robust) GWLMM Fits

In baldermann/rsaeGWR: Robust small area estimation under spatial non-stationarity

Description

Interface for predicting small area means based on a gwlmm ( or rgwlmm) model fit.

Usage

## S3 method for class 'gwlmm'
predict(object, popdata = NULL, size = NULL,
  popAgg = TRUE, ...)

## S3 method for class 'rgwlmm'
predict(object, popdata = NULL, size = NULL,
  popAgg = TRUE, bcConst = 3, maxit = 100, tol = 1e-04, ...)

Arguments

object	(formula) object of class 'gwlmm' or 'rgwlmm'
popdata	(data.frame) an optional data frame (Default = NULL). If ommited, in-sample prdictions are estimated.
size	(character) name for the column in popdata containing the area-specific population sizes (Default = NULL). Obligatory when popAgg = TRUE.
popAgg	(logical) TRUE if popdata is aggregated and only contains area level information
...	not used
bcConst	(numeric) needed for objects of class rgwlmm. Defines the tuning constant for influience function in the bias correction term (default = 3). Ses datails.
maxit	(integer) needed for objects of class rgwlmm. Defines the maximum number of iterations for the estiamtion of the random effects for rgwlmm objects (default = 100).
tol	(numeric) needed for objects of class rgwlmm. Defines the tolerance for the convergence of the fitting process (default = 1e-04).

Details

• The argument popdata can have three different definitions: (1) popdata = NULL, (2) popdata is a data frame for aggregated population information, (3) popdata is a data frame for unit-level population information. In case (1) only in-sample predictions are estimated. In case (2) the size argument is obligatory. In case (3) popAgg must be TRUE. Population data can contain non-sampled areas.

• The method predict is implemented for three combinations of geographic information in the sampled (S) and population (P) data: (1) only centroid information in S and P; (2) unit-level geographic information in S and P; (3) unit-level geographic information in S and centriod informaton in P.

• For objects of class gwlmm: the MSE estimates for the small area means returned in areaEst are named CCT and CCST. The former is based on pseudo-linearization following Chambers et al. (2011), and latter is linearization-based following Chambers et al. (2014).

• For objects of class rgwlmm: the MSE estimates for the small area means returned in areaEst are named CCT (and CCT_bc) and CCST ( and CCST_bc). The subscript _bc indicates the respective MSE estimate for bias corrected robust area mean. The MSE estimates are based on the pseudo-linearizetion (CCT) and the linearization-based approach in Chambers et al. (2014).

• For objects of class rgwlmm: the bias correction is based on the area-specific prediction error where the influence of extreme values is restricted using Huber's influence function. cbConst defines this restriction but should be less restrictive the k in rgwlmm. By default it is set cbConst = 3.

Value

The function predict.gwlmm returns a list containing the predictions

If popdata = NULL, a list with the following elements is returned.

• call (language) the call generating the value

• nIter (numeric) number of iterations needed for the estimation of the random effects (only for rgwlmm-objects)

• raneff (numeric) named vector of random effects

• residuals (numeric) vector of restimated residuals

• prediction (numeric) vector of estimated in-sample predicted values

• xbeta (numeric) vector of estimated fixed part of the in-sample predictions

If popdata is a data.frame a list with the following elements is returned.

• call (language) the call generating the value

• nIter (numeric) number of iterations needed for the estimation of the random effects (only for rgwlmm-objects)

• areaEst (data.frame) a data frame containing area-specific mean predictions and MSE estimates.

• ranEff (data.farme) a data frame containing the random effects.

• sampleEst (data.frame) a data frame containing the in-sample predictions (prediction, residuals, xbeta)

References

Chambers, R., J. Chandra, and N. Tzavidis (2011). On bias-robust mean squared error estimation for pseudo-linear small area estimators. Survey Methodology 37 (2), 153 - 170.

Chambers, R., H. Chandra, N. Salvati, and N. Tzavidis (2014). Outlier robust small area estimation. Journal of the Royal Statistical Society: Series B 76 (1), 47 - 69.

See Also

rgwlmm, and gwlmm

Examples

# Data sets ?sampleData, ?popaggData and ?popoutData are
# implemented in the rsarGWR-package. See help files.

## Not run: 

formula <- y~1+x|clusterid |long + lat

#Model fit
gwmodel<-gwlmm(formula, data = data)

#In-sample predictions
pred<-predict(gwmodel)

#Small area mean prediction for aggregated population data
predagg<-predict(gwmodel, popdata = popaggData, size = "Size")

#Small area mean prediction for unit-level population data
preddisagg<-predict(gwmodel, popdata = popoutData, popAgg = FALSE)

## End(Not run)
##################################################################
# Outlier-robust estimation
## Not run: 

# Model fit
rgwmodel<- rgwlmm(formula, data = sampleData)

# In-sample prediction
rpred<-predict(rgwmodel)
#Small area preditions (mean) for aggregated population data
rpredagg<-predict(rgwmodel, popdata = popaggData, size = "Size")
#Small area preditions (mean) for unit-level population data
rpreddisagg<-predict(rgwmodel, popdata = popoutData, popAgg = FALSE)

###########

# Robust model fit when sample only contains centroid information
rgwmodel<- rgwlmm(formula, data = sampleData, centroid = TRUE)

# In-sample prediction
rpred<-predict(rgwmodel)
#Small area means for aggregated population data
rpredagg<-predict(rgwmodel, popdata = popaggData, size = "Size")


## End(Not run)

baldermann/rsaeGWR documentation built on May 6, 2019, 2:19 p.m.