# varianceMatrices: Matrix constructor functions In wahani/saeRobustTools: Robust Small Area Estimation

## Description

These functions construct different parts of matrix components. They are used internally. If you are interested in the weights of a model fitted using rfh please try to use weights.fitrfh on that object.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```matU(.V) matTrace(x) matB(y, X, beta, re, matV, psi) matBConst(y, X, beta, matV, psi) matA(y, X, beta, matV, psi) matAConst(y, X, matV, psi) matW(y, X, beta, re, matV, psi) matWbc(y, reblup, W, samplingVar, c = 1) matTZ(.nDomains, .nTime) matTZ1(.nDomains = 10, .nTime = 10) ```

## Arguments

 `.V` (Matrix) variance matrix `x` ([m|M]atrix) a matrix `y` (numeric) response `X` (Matrix) design matrix `beta` (numeric) vector of regression coefficients `re` (numeric) vector of random effects `matV` (list of functions) see `matVFH` for an example `psi` (function) the influence function `reblup` (numeric) vector with robust best linear unbiased predictions `W` (Matrix) the weighting matrix `samplingVar` (numeric) the vector of sampling variances `c` (numeric) scalar `.nDomains` (integer) number of domains `.nTime` (integer) number of time periods

## Details

`matU` computes U. U is the matrix containing only the diagonal elements of V. This function returns a list of functions which can be called to compute specific transformations of U.

`matTrace` computes the trace of a matrix.

`matB` computes the matrix B which is used to compute the weights in the pseudo linearised representation of the REBLUP.

`matBConst` returns a function with one argument, u, to compute the matrix B. This function is used internally to compute B in the fixed point algorithm.

`matA` computes the matrix A which is used to compute the weights in the pseudo linearized representation of the REBLUP.

`matAConst` returns a function with one argument, beta, to compute the matrix A. This function is used internally to compute A in the fixed point algorithm for beta.

`matW` returns a matrix containing the weights as they are defined for the pseudo linear form, such that `matW %*% y` is the REBLUP.

`matWbc` returns a matrix containing the weights as they are defined for the pseudo linear form, such that `matWbc %*% y` is the bias-corrected REBLUP. `c` is a multiplyer for the standard deviation.

`matTZ` constructs the Z matrix in a linear mixed model with autocorrelated random effects.

`matTZ1` constructs the Z1 matrix in a linear mixed model with autocorrelated random effects.

## References

Warnholz, S. (2016): "Small Area Estimaiton Using Robust Extension to Area Level Models". Not published (yet).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37``` ```data("grapes", package = "sae") data("grapesprox", package = "sae") fitRFH <- rfh( grapehect ~ area + workdays - 1, data = grapes, samplingVar = "var" ) matV <- variance(fitRFH) # matU: matU(matV\$V())\$U() matU(matV\$V())\$sqrt() matU(matV\$V())\$sqrtInv() # matB (and matA + matW accordingly): matB( fitRFH\$y, fitRFH\$x, fitRFH\$coefficients, fitRFH\$re, matV, function(x) psiOne(x, k = fitRFH\$k) ) matBConst( fitRFH\$y, fitRFH\$x, fitRFH\$coefficients, matV, function(x) psiOne(x, k = fitRFH\$k) )(fitRFH\$re) # construcors for 'Z' in linear mixed models matTZ(2, 3) matTZ1(2, 3) ```

wahani/saeRobustTools documentation built on May 3, 2019, 8:09 p.m.