CovMat: Covariance Matrix for Spatial Models

In RcppCensSpatial: Spatial Estimation and Prediction for Censored/Missing Responses

Description

This function computes the spatial variance-covariance matrix considering exponential, gaussian, matern, or power exponential correlation functions.

Usage

CovMat(phi, tau2, sigma2, dist, type = "exponential", kappa = 0)

Arguments

phi	spatial scaling parameter.
tau2	nugget effect parameter.
sigma2	partial sill parameter.
dist	n x n distance matrix.
type	type of spatial correlation function: 'exponential', 'gaussian', 'matern', and 'pow.exp' for exponential, gaussian, matern, and power exponential, respectively.
kappa	parameter for all spatial correlation functions. For exponential and gaussian κ=0, for power exponential 0 < κ <= 2, and for matern correlation function κ > 0.

Details

The spatial covariance matrix is given by

Σ = [Cov(s_i, s_j )] = σ^2 R(φ) + τ^2 I_n,

where σ^2 > 0 is the partial sill, φ > 0 is the spatial scaling parameter, τ^2 is known as the nugget effect in the geostatistical framework, R(φ) is the n x n correlation matrix computed from the correlation function, and I_n is the n x n identity matrix.

The spatial correlation functions available are:

Exponential:

Corr(d) = exp(-d/φ),

Gaussian:

Corr(d) = exp(-(d/φ)^2),

Matern:

Corr(d) = 1/(2^(κ-1)Γ(κ))(d/φ)^κ K_κ(d/φ),

Power exponential:

Corr(d) = exp(-(d/φ)^κ),

where d >= 0 is the Euclidean distance between two observations, Γ(.) is the gamma function, κ is the smoothness parameter, and K_κ(.) is the modified Bessel function of the second kind of order κ.

Value

The function returns the n x n spatial covariance matrix.

Author(s)

Katherine L. Valeriano, Alejandro Ordonez, Christian E. Galarza and Larissa A. Matos.

See Also

EM.sclm, SAEM.sclm, MCEM.sclm, dist2Dmatrix

Examples

# Initial parameter values
phi = 5;  tau2 = 0.80;  sigma2 = 2
n = 20
set.seed(1000)
x = round(runif(n,0,10), 5)     # X coordinate
y = round(runif(n,0,10), 5)     # Y coordinate
Ms = dist2Dmatrix(cbind(x, y))
Cov = CovMat(phi, tau2, sigma2, Ms, "exponential", 0)

RcppCensSpatial documentation built on Sept. 21, 2021, 5:07 p.m.