CovarianceM {StempCens}

Covariance matrix for spatio-temporal model

Description

It computes the spatio-temporal covariance matrix for balanced data, i.e., when we have the same temporal indexes per location. To compute the spatial correlation it provides 5 functions: exponential, gaussian, matern, spherical and power exponential. To compute the temporal correlation is used an autocorrelation function of an AR(1) process.

Usage

CovarianceM(phi, rho, tau2, sigma2, distSpa, disTemp, kappa, type.S)

Arguments

phi

value of the spatial scaling parameter.

rho

value of the time scaling parameter.

tau2

value of the the nugget effect parameter.

sigma2

value of the partial sill.

distSpa

n x n spatial distance matrix without considering repetitions.

disTemp

T x T temporal distance matrix without considering repetitions.

kappa

parameter for all spatial covariance functions. In the case of exponential, gaussian and spherical function \kappa is equal to zero. For the power exponential function \kappa is a number between 0 and 2. For the matern correlation function is upper than 0.

type.S

type of spatial correlation function: 'exponential' for exponential, 'gaussian' for gaussian, 'matern' for matern, 'pow.exp' for power exponential and 'spherical' for spherical function, respectively. See the analytical form of these functions in EffectiveRange.

Value

The function returns the nT x nT spatio-temporal covariance matrix for balanced data.

Author(s)

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

Examples

# Initial parameter values
phi <- 5;     rho <- 0.45
tau2 <- 0.80; sigma2 <- 2
# Simulating data
n1 <- 10   # Number of spatial locations
n2 <- 5    # Number of temporal index
set.seed(1000)
x.co <- round(runif(n1,0,10),5)  # X coordinate
y.co <- round(runif(n1,0,10),5)  # Y coordinate
coord <- cbind(x.co,y.co)        # Cartesian coordinates without repetitions
time <- as.matrix(seq(1,n2))     # Time index without repetitions
# Covariance matrix
Ms <- as.matrix(dist(coord))     # Spatial distances
Mt <- as.matrix(dist(time))      # Temporal distances
Cov <- CovarianceM(phi,rho,tau2,sigma2,distSpa=Ms,disTemp=Mt,kappa=0,type.S="exponential")