Simulation study

gs <- expand.grid((0:10)/10, (0:10)/10)
niter <- 100
arr <- array(NA, dim=c(niter, 2, 2), dimnames=list(niter=1:niter, stat=c("beta","beta.var"), dep=c(1,0)))
 
# gau
set.seed(111)
gd <- grf(grid=gs, cov.pars=c(1,0.2), mean=2, nsim=niter)
 
for(i in 1:niter){
cat(i)
	ggdd <- gd
	ggdd$data <- gd$data[,i]
	lf <- likfit(ggdd, ini.cov.pars=c(1,0.2), messages=FALSE)
	arr[i,,1] <- c(lf$beta, lf$beta.var)
}
 
# gau independente
set.seed(111)
gd <- grf(grid=gs, cov.pars=c(0,0), mean=2, nsim=niter, nugget=1)
 
for(i in 1:niter){
cat(i)
	ggdd <- gd
	ggdd$data <- gd$data[,i]
	lf <- likfit(ggdd, ini.cov.pars=c(0.5,0.5), messages=F)
	arr[i,,2] <- c(lf$beta, lf$beta.var)
}
 
pdf("betabias.pdf")
par(mfrow=c(2,2))
hist(arr[,1,1], main="beta for mu=2 s2=1 phi=0.2 t2=0")
hist(arr[,1,2], main="beta for mu=2 s2=0 phi=0 t2=1")
hist(arr[,2,1], main="beta.var")
hist(arr[,2,2], main="beta.var")
dev.off()

## Modelo: variáveis com mu dependente e correlação componente espacial parcialmente comum
##	Y1 = mu1 + S00 + S11 + e1 = mu1 + sig00 R + sig11 R11 + e1
##	Y2 = mu2 + S00 + S22 + e2 = mu1 + sig00 R + sig22 R22 + e2
##	Y3 = mu3 + S00 + S33 + e3 = mu1 + sig00 R + sig33 R33 + e3
##	Constraint by: 
##		sig00 + sig## = 1; e# = 1
##		mu ~ MVG(c(mu1, mu2, mu3), Sigma)
##		mu1 = mu2 = mu3 = 1
##		diag(Sigma) = e# 

i indexa localizações j indexa idades

• Definir grid
• Definir sig00 (usado para gerir associação espacial entre idades)
• Simular Ij gaussiana
  • set sig00 e phi00 = sig00/5
  • set sig## = 1-sig00 e phi## = sig##/5
  • set mu## = 0.4
  • sim S ~ MVN(0,Sig) Sig=f(sig, phi)
  • sim mu ~ MVN({mu1,mu2,m3}, Sigmu) Sigmu = {indep, dep}
  • set Ij = muj + S00 + Sjj
• Construir Y = prod(exp{Ij})
• Construir Pj = exp{Ij}/sum_j(exp{Ij})
• Construir Ij = Y*Pj para garantir que Y = sum_j(Ij)
• Aleatorizar vector de localizações (100)
• Construir amostras de Y, P e I
• Ajustar modelo geo
• Estimar Y
  • Yhat = exp{beta+beta.var/2}
  • Ybar = sum_i(Yi)/n
• Estimar Ij
  • Ihatj = Yhat * 1/n sum_i(Pij) sendo Pij = Iij/sum_j(Iij)
  • Ibarj = sum_i(Iij)/n