PredStempCens function

Prediction in spatio-temporal model with censored/missing responses

This function performs spatio-temporal prediction in a set of new S spatial locations for fixed time points.

PredStempCens(Est.StempCens, locPre, timePre, xPre)

Arguments

• Est.StempCens: an object of class Est.StempCens given as output by the EstStempCens function.
• locPre: a matrix of coordinates for which prediction is performed.
• timePre: the time point vector for which prediction is performed.
• xPre: a matrix of covariates for which prediction is performed.

Returns

The function returns an object of class Pred.StempCens which is a list given by:

• predValues: predicted values.

• VarPred: predicted covariance matrix.

Examples

## Not run:

# Initial parameter values
beta <- c(-1,1.50)
phi  <- 5;    rho <- 0.60
tau2 <- 0.80; sigma2 <- 2
# Simulating data
n1 <- 17   # Number of spatial locations
n2 <- 5    # Number of temporal index
set.seed(12345)
x.co <- round(runif(n1,0,10),9)   # X coordinate
y.co <- round(runif(n1,0,10),9)   # Y coordinate
coord <- cbind(x.co,y.co)         # Cartesian coordinates without repetitions
coord2 <- cbind(rep(x.co,each=n2),rep(y.co,each=n2)) # Cartesian coordinates with repetitions
time <- as.matrix(seq(1,n2))      # Time index without repetitions
time2 <- as.matrix(rep(time,n1))  # Time index with repetitions
x1 <- rexp(n1*n2,2)
x2 <- rnorm(n1*n2,2,1)
x  <- cbind(x1,x2)
media <- x%*%beta
# Covariance matrix
Ms  <- as.matrix(dist(coord))   # Spatial distances
Mt  <- as.matrix(dist(time))    # Temporal distances
Cov <- CovarianceM(phi,rho,tau2,sigma2,Ms,Mt,0.50,"pow.exp")
# Data
require(mvtnorm)
y <- as.vector(rmvnorm(1,mean=as.vector(media),sigma=Cov))
data <- data.frame(coord2,time2,y,x)
names(data) <- c("x.coord","y.coord","time","yObs","x1","x2")
# Splitting the dataset
local.est  <- coord[-c(4,13),]
data.est   <- data[data$x.coord%in%local.est[,1]&data$y.coord%in%local.est[,2],]
data.valid <- data[data$x.coord%in%coord[c(4,13),1]&data$y.coord%in%coord[c(4,13),2],]
# Censored
perc <- 0.10
y <- data.est$yObs
aa <- sort(y);  bb <- aa[1:(perc*nrow(data.est))]
cutof <- bb[perc*nrow(data.est)]
cc <- matrix(1,nrow(data.est),1)*(y<=cutof)
y[cc==1] <- cutof
data.est <- cbind(data.est[,-c(4,5,6)],y,cc,data.est[,c(5,6)])
names(data.est) <- c("x.coord","y.coord","time","yObs","censored","x1","x2")

# Estimation
y  <- data.est$yObs
x  <- cbind(data.est$x1,data.est$x2)
cc <- data.est$censored
time2  <- matrix(data.est$time)
coord2 <- data.est[,1:2]
LI <- y; LI[cc==1] <- -Inf    # Left-censored
LS <- y
est_teste <- EstStempCens(y, x, cc, time2, coord2, LI, LS, init.phi=3.5,
                 init.rho=0.5, init.tau2=1, kappa=0.5, type.S="pow.exp",
                 IMatrix=FALSE, M=20, perc=0.25, MaxIter=300, pc=0.20)
class(est_teste)

# Prediction
locPre <- data.valid[,1:2]
timePre <- matrix(data.valid$time)
xPre <- cbind(data.valid$x1,data.valid$x2)
pre_teste <- PredStempCens(est_teste, locPre, timePre, xPre)
library(ggplot2)
Model <- rep(c("y Observed","y Predicted"),each=10)
station <- rep(rep(c("Station 1", "Station 2"),each=5),times=2)
xcoord1 <- rep(seq(1:5),4)
ycoord1 <- c(data.valid$yObs,pre_teste$predValues)
data2 <- data.frame(Model,station,xcoord1,ycoord1)
ggplot(data=data2,aes(x=xcoord1,y=ycoord1)) + geom_line(aes(color=Model)) +
facet_wrap(station~.,nrow=2) + labs(x="",y="") + theme(legend.position="bottom")
## End(Not run)

See Also

EstStempCens

Author(s)

Katherine L. Valeriano, Victor H. Lachos and Larissa A. Matos