###############################################################
# A simulated data: mixture of two normals
###############################################################
rm(list=ls())
library(MASS)
library(Rcpp)
library(RcppArmadillo)
library(coda)
library(survival)
library(spBayesSurv)
## True parameters
betaT = cbind(c(3.5, 0.5), c(2.5, -1));
wT = c(0.4, 0.6);
sig2T = c(1^2, 0.5^2);
theta1 = 0.98; theta2 = 0.1;
## generate coordinates:
## npred is the # of locations for prediction
n = 300; npred = 30; ntot = n + npred;
ldist = 100; wdist = 40;
s1 = runif(ntot, 0, wdist); s2 = runif(ntot, 0, ldist);
s = rbind(s1,s2);
#plot(s[1,], s[2,]);
## divide them into blocks
nldist=10; nwdist=4;
nb=nldist*nwdist; nb; # number of blocks;
coor = matrix(0, nb, 4); ## four edges for each block;
tempindex=1; lstep=ldist/nldist; wstep=wdist/nwdist;
for(i in 1:nwdist){
for(j in 1:nldist){
coor[tempindex,] = c((i-1)*wstep, i*wstep, (j-1)*lstep, j*lstep );
tempindex = tempindex + 1;
}
}
## Assign block id for each location
blockid = rep(NA,ntot);
for(i in 1:nb){
blockid[((s1>coor[i,1])*(s1<=coor[i,2])*(s2>coor[i,3])*(s2<=coor[i,4]))==1]=i;
}
## Choose knots S*
nldist=15; nwdist=6;
m=nldist*nwdist; m; # number of knots;
ss = matrix(0, m, 2);
tempindex=1; lstep=ldist/nldist; wstep=wdist/nwdist;
for(i in 1:nwdist){
for(j in 1:nldist){
ss[tempindex,] = c( (i-1)*wstep+wstep/2, (j-1)*lstep+lstep/2);
tempindex = tempindex + 1;
}
}
## Covariance matrix
dnn = .Call("DistMat", s, s, PACKAGE = "spBayesSurv");
corT = theta1*exp(-theta2*dnn)+(1-theta1)*diag(ntot);
## Generate x
x = runif(ntot,-1.5,1.5);
X = cbind(rep(1,ntot), x);
p = ncol(X); # number of covariates + 1
## Generate transformed log of survival times
z = mvrnorm(1, rep(0, ntot), corT);
## The pdf of Ti:
fi = function(y, xi, w=wT){
nw = length(w);
ny = length(y);
res = matrix(0, ny, nw);
Xi = c(1,xi);
for (k in 1:nw){
res[,k] = w[k]*dnorm(y, sum(Xi*betaT[,k]), sqrt(sig2T[k]) )
}
apply(res, 1, sum)
}
## true plot
xx = seq(-2, 7, 0.01)
plot(xx, fi(xx, -1), "l", lwd=2, col=2)
lines(xx, fi(xx, 1), "l", lwd=2, col=3)
## The CDF of Ti:
Fi = function(y, xi, w=wT){
nw = length(w);
ny = length(y);
res = matrix(0, ny, nw);
Xi = c(1,xi);
for (k in 1:nw){
res[,k] = w[k]*pnorm(y, sum(Xi*betaT[,k]), sqrt(sig2T[k]) )
}
apply(res, 1, sum)
}
## The inverse for CDF of Ti
Finvsingle = function(u, xi) {
res = uniroot(function (x) Fi(x, xi)-u, lower=-500, upper=500);
res$root
}
Finv = function(u, xi) {sapply(u, Finvsingle, xi)};
## Generate log of survival times y
u = pnorm(z);
y = rep(0, ntot);
for (i in 1:ntot){
y[i] = Finv(u[i], x[i]);
}
#plot(x,y);
yTrue = y;
## Censoring scheme
Centime = runif(ntot, 3.5,5);
Centime = 10000;
delta = (y<=Centime) +0 ;
sum(delta)/ntot;
cen = which(delta==0);
y[cen] = Centime[cen];
## make a data frame
dtotal = data.frame(s1=s1, s2=s2, y=y, x=x, delta=delta, yTrue=yTrue, id=blockid);
## Hold out npred=30 for prediction purpose
predindex = sample(1:ntot, npred);
dpred = dtotal[predindex,];
dtrain = dtotal[-predindex,];
# rename the variables
d = dtrain; n=nrow(d); n;
s = cbind(d$s1, d$s2);
y = d$y;
x = d$x;
delta =d$delta;
# FSA settings
knots = list(ss=ss, blockid=d$id);
# Prediction settings
xpred = dpred$x;
s0 = cbind( dpred$s1, dpred$s2 );
prediction = list(spred=s0, xpred=xpred, predid=dpred$id);
###############################################################
# spatial copula DDP
###############################################################
# MCMC parameters
nburn <- 1000
nsave <- 500
nskip <- 4
ndisplay <- 100
mcmc <- list(nburn=nburn,
nsave=nsave,
nskip=nskip,
ndisplay=ndisplay)
# Prior information
prior = list(N = 10,
m0 = rep(0,p),
S0 = diag(rep(1e5,p), nrow=p, ncol=p),
Sig0 = diag(rep(1e5,p), nrow=p, ncol=p),
k0 = 7,
nua = 2, nub = 1,
a0 = 1, b0 = 1,
spS0 = diag(c(4,4)),
spadapter = 1,
theta0 = c(1.0, 1.0, 0.5, 0.2));
# current state values
state <- list(theta=c(0.95, 0.5));
# Fit the model
fitspDDP = spCopulaDDP( y = y,
delta =delta,
x = x,
s = s,
prediction=prediction,
prior=prior,
mcmc=mcmc,
state=state,
FSA=FALSE,
knots=knots);
res = fitspDDP; remove(fitspDDP);
# trace plots
par(mfrow = c(3,2))
w.save2 = res$w;
Kindex = which.max(rowMeans(w.save2));
traceplot(mcmc(w.save2[Kindex,]), main="w")
sig2.save2 = res$sigma2;
traceplot(mcmc(sig2.save2[Kindex,]), main="sig2")
beta.save2 = res$beta;
alpha.save2 = res$alpha;
traceplot(mcmc(beta.save2[2,Kindex,]), main="beta")
traceplot(mcmc(alpha.save2), main="alpha")
theta1.save2 = res$theta1;
theta2.save2 = res$theta2
traceplot(mcmc(theta1.save2), main="theta1")
traceplot(mcmc(theta2.save2), main="theta2")
## LPML
LPML2 = sum(log(res$cpo)); LPML2;
## MSPE
mean((dpred$yTrue-apply(res$Ypred, 1, median))^2);
## plots
par(mfrow = c(2,2));
xnew = c(-1, 1);
xpred = cbind(xnew);
nxpred = nrow(xpred);
ygrid = seq(0,6.0,0.05); tgrid = exp(ygrid);
ngrid = length(ygrid);
estimates = GetCurves(res, xpred, ygrid, CI=c(0.05, 0.95));
fhat = estimates$fhat;
Shat = estimates$Shat;
## density in y
plot(ygrid, fi(ygrid, xnew[1]), "l", lwd=2, ylim=c(0, 0.8),
xlim=c(0,6), main="density in y")
for(i in 1:nxpred){
lines(ygrid, fi(ygrid, xnew[i]), lwd=2)
lines(ygrid, fhat[,i], lty=2, lwd=2, col=4);
}
## survival in y
plot(ygrid, 1-Fi(ygrid, xnew[1]), "l", lwd=2, ylim=c(0, 1),
xlim=c(0,6), main="survival in y")
for(i in 1:nxpred){
lines(ygrid, 1-Fi(ygrid, xnew[i]), lwd=2)
lines(ygrid, Shat[,i], lty=2, lwd=2, col=4);
}
## density in t
plot(tgrid, fi(ygrid, xnew[1])/tgrid, "l", lwd=2, ylim=c(0, 0.15),
xlim=c(0,100), main="density in t")
for(i in 1:nxpred){
lines(tgrid, fi(ygrid, xnew[i])/tgrid, lwd=2)
lines(tgrid, fhat[,i]/tgrid, lty=2, lwd=2, col=4);
}
## survival in t
plot(tgrid, 1-Fi(ygrid, xnew[1]), "l", lwd=2, ylim=c(0, 1),
xlim=c(0,100), main="survival in t")
for(i in 1:nxpred){
lines(tgrid, 1-Fi(ygrid, xnew[i]), lwd=2)
lines(tgrid, Shat[,i], lty=2, lwd=2, col=4);
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