SpTe2M (version 1.0.3)

sim_dat: A simulated spatio-temporal dataset

Description

This simulated dataset is saved as a list, and it contains the following three elements:

y

A vector of length \(N\); it contains the data of the observed response variable \(y\).

x

A vector of length \(N\); it contains the data of the covariate \(x\).

st

An \(N\times 3\) matrix containing the spatial locations and times for all the observations in the dataset.

Usage

data(sim_dat)

Format

A list containing \(N=10,000\) observations.

Author

Kai Yang and Peihua Qiu

Examples

library(MASS)
set.seed(100)
n <- 100; m <- 100; N <- n*m
t <- rep(seq(0.01,1,0.01),each=m)
su <- sv <- seq(0.1,1,0.1)
su <- rep(su,each=10); sv <- rep(sv,10)
su <- rep(su,n); sv <- rep(sv,n)
st <- matrix(0,N,3)
st[,1] <- su; st[,2] <- sv; st[,3] <- t
mu <- rep(0,N)
for(i in 1:N) {
  mu[i] <- 2+sin(pi*su[i])*sin(pi*sv[i])+sin(2*pi*t[i]) 
}
dist <- matrix(0,m,m) # distance matrix
for(i in 1:m) {
  for(j in 1:m) {
    dist[i,j] <- sqrt((su[i]-su[j])^2+(sv[i]-sv[j])^2)
  }
}
cov.s <- matrix(0,m,m) # spatial correlation
for(i in 1:m) {
  for(j in 1:m) {
    cov.s[i,j] <- 0.3^2*exp(-30*dist[i,j]) 
  }
}
noise <- matrix(0,n,m)
noise[1,] <- MASS::mvrnorm(1,mu=rep(0,m),Sigma=cov.s) 
for(i in 2:n) {
  noise[i,] <- 0.1*noise[i-1,]+sqrt(1-0.1^2)*
    MASS::mvrnorm(1,mu=rep(0,m),Sigma=cov.s)
}
noise <- c(t(noise)); x <- rnorm(N,0,0.3) 
beta <- 0.5; y <- mu+x*beta+noise
sim_dat <- list(); sim_dat$y <- y
sim_dat$x <- x; sim_dat$st <- st