Description Usage Arguments Details Value Author(s) See Also Examples
View source: R/AuxiliaryFunctions_USER.R
This function computes the spatial variance-covariance matrix considering exponential, gaussian, matern, or power exponential correlation functions.
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phi |
spatial scaling parameter. |
tau2 |
nugget effect parameter. |
sigma2 |
partial sill parameter. |
dist |
n x n distance matrix. |
type |
type of spatial correlation function: ' |
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. |
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:
Corr(d) = exp(-d/φ),
Corr(d) = exp(-(d/φ)^2),
Corr(d) = 1/(2^(κ-1)Γ(κ))(d/φ)^κ K_κ(d/φ),
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.
The function returns the n x n spatial covariance matrix.
Katherine L. Valeriano, Alejandro Ordonez, Christian E. Galarza and Larissa A. Matos.
EM.sclm
, SAEM.sclm
, MCEM.sclm
, dist2Dmatrix
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