# R/cormat.R In gcmr: Gaussian Copula Marginal Regression

#### Documented in arma.cormatcluster.cormatind.cormatmatern.cormat

```## cormat must have class cormat.gcmr and the following elements:
## - npar: number of parameters.
## - start(): initial estimates; optional attributes lower and upper can be used
##   to specify box constrained parameters
## - chol(tau,not.na): returns the cholesky factor of the correlation matrix
##   (only for the not.na observations; not.na is a logical vector)
##   This function should return NULL if tau is outside parameter space

## working independence correlation
ind.cormat <- function() {
ans <- list()
ans\$npar <- 0
ans\$independent <- TRUE
ans\$start <- function() double(0)
ans\$chol <- function(tau , not.na) diag(rep(1,sum(not.na)))
class( ans ) <- c("ind.gcmr", "cormat.gcmr")
ans
}

## arma(p,q) correlation for time-series
arma.cormat <- function( p=0 , q=0 ) {
if(p==0 && q==0)
return( ind.cormat() )
iar <- if ( p ) 1:p else NULL
ima <- if ( q ) (p+1):(p+q) else NULL
ans <- list()
ans\$npar <- p+q
ans\$start <- function() {
tau <- rep(0, p+q)
names(tau) <- c(if ( p ) paste("ar",1:p,sep="") else NULL ,
if ( q ) paste("ma",1:q,sep="") else NULL )
tau
}
ans\$chol <- function( tau , not.na ) {
if ( ( p && any(Mod(polyroot(c(1,-tau[iar])))<1.01) ) ||
( q && any(Mod(polyroot(c(1, tau[ima])))<1.01) ) )
return( NULL )
n <- length(not.na)
rho <- ARMAacf(tau[iar],tau[ima],n-1)
r <- seq(1,n)[not.na]
chol(outer( r , r , function(i,j) rho[1+abs(i-j)] ))
}
class( ans ) <- c("arma.gcmr", "cormat.gcmr")
ans
}

## clustered data
## assume that it is not possible that all the observations inside a cluster
## can be missing
cluster.cormat <- function(id, type=c("independence", "ar1", "ma1",
"exchangeable", "unstructured")) {
type <- match.arg(type)
if(!length(rle(id)\$values)==length(unique(id)))
stop("data must be sorted in way that observations from the same cluster are contiguous")
ng <- 1:length(unique(id))
if (!(length(ng)>1)) stop("only one strata")
if (type=="independence") {
ans <- ind.cormat()
ans\$id <- id
return(ans)
}
ans <- list(type=type,id=id)
ans\$npar <-  if(type!="unstructured") 1 else choose(max(table(id)), 2)
data <- data.frame(id=id)
fn <- switch(type,
"ar1"=function(g) nlme::corAR1(g, form= ~1|id),
"ma1"=function(g) nlme::corARMA(g, form= ~1|id, p=0, q=1),
"exchangeable"=function(g) nlme::corCompSymm(g, form= ~1|id),
"unstructured"=function(g) nlme::corSymm(g, form= ~1|id))
ans\$start <- function() {
np <-  if(type!="unstructured") 1 else choose(max(table(id)), 2)
tau <- rep(0, np)
names(tau) <- switch(type, "ar1"="ar1", "ma1"="ma1", "exchangeable"="tau",
"unstructured"=paste("tau", 1:ans\$npar, sep=""))
eps <- sqrt(.Machine\$double.eps)
attr(tau,"lower") <- rep(-1+eps,np)
attr(tau,"upper") <- rep(1-eps,np)
tau
}
ans\$chol <- function(tau, not.na) {
q <- try(nlme::corMatrix(nlme::Initialize(fn(tau),data=data)),silent=TRUE)
if (inherits(q,"try-error")) return(NULL)
g <- split(not.na,id)
q <- try(lapply(ng,function(i) chol(q[[i]][g[[i]],g[[i]]])),silent=TRUE)
if (inherits(q,"try-error") ) NULL else q
}
class( ans ) <- c("cluster.gcmr", "cormat.gcmr")
ans
}

## Matern correlation for spatial data
## D is a distance matrix, alpha is the smoothing parameter
matern.cormat <- function(D, alpha=0.5) {
ans <- list()
ans\$npar <- 1
ans\$start <- function() {
tau <- median(D)
names(tau) <- c("tau")
attr(tau,"lower") <- sqrt(.Machine\$double.eps)
tau
}
ans\$chol <- function( tau, not.na ){
S <- geoR::matern(D, tau, alpha)
q <- try(chol(S[not.na,not.na]),silent=TRUE)
if( inherits(q,"try-error") ) NULL else q
}
class( ans ) <- c("matern.gcmr", "cormat.gcmr")
ans
}
```

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gcmr documentation built on April 30, 2018, 5:03 p.m.