Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/EstSAEMspatial_USER.R
This function returns the maximum likelihood (ML) estimates of the unknown parameters in Gaussian spatial models with censored/missing responses via the SAEM algorithm. It supports left, right, interval, or missing values in the dependent variable. It also computes the observed information matrix using the method developed by \insertCitelouis1982finding;textualRcppCensSpatial.
1 2 3 4 
y 
vector of responses. 
x 
design matrix. 
cens 
vector of censoring indicators. For each observation: 
LI 
lower limit of detection. For each observation: if noncensored 
LS 
upper limit of detection. For each observation: if noncensored 
coords 
2D spatial coordinates. 
init.phi 
initial value for the spatial scaling parameter. 
init.nugget 
initial value for the nugget effect parameter. 
type 
type of spatial correlation function: ' 
kappa 
parameter for all spatial correlation functions. See 
lower, upper 
vectors of lower and upper bounds for the optimization method. If unspecified, the default is

MaxIter 
maximum number of iterations of the SAEM algorithm. By default 
M 
number of Monte Carlo samples for stochastic approximation. By default 
pc 
percentage of iterations of the SAEM algorithm with nomemory. By default 
error 
maximum convergence error. By default 
show.SE 

The spatial Gaussian model is given by
Y = Xβ + ξ,
where Y is the n x 1 vector of response, X is the n x q design matrix, β is the q x 1 vector of regression coefficients to be estimated, and ξ is the error term which is normally distributed with zeromean and covariance matrix Σ=σ^2 R(φ) + τ^2 I_n. We assume that Σ is nonsingular and X has full rank \insertCitediggle2007springerRcppCensSpatial.
The estimation process was performed via the SAEM \insertCitedelyon1999convergenceRcppCensSpatial algorithm.
The spatial SAEM algorithm was previously proposed by \insertCitelachos2017influence;textualRcppCensSpatial
and \insertCiteordonez2018geostatistical;textualRcppCensSpatial and is available in package CensSpatial
.
The difference between this package to CensSpatial
is that the random observations are sampled
through the slice sampling algorithm available in package relliptical
and the optimization procedure
by the roptim
package.
This model is also a particular case of the Spatiotemporal model defined by \insertCitevaleriano2021likelihood;textualRcppCensSpatial,
when the number of temporal observations is equal to one. The computing codes of the Spatiotemporal
SAEM algorithm are available in the package StempCens
.
The function returns an object of class sclm
which is a list given by:
Theta 
estimated parameters in all iterations, θ = (β, σ^2, φ, τ^2). 
theta 
final estimation of θ = (β, σ^2, φ, τ^2). 
beta 
estimated β. 
sigma2 
estimated σ^2. 
phi 
estimated φ. 
tau2 
estimated τ^2. 
EY 
stochastic approximation of the first moment for the truncated normal distribution. 
EYY 
stochastic approximation of the second moment for the truncated normal distribution. 
SE 
vector of standard errors of θ = (β, σ^2, φ, τ^2). 
InfMat 
observed information matrix. 
loglik 
loglikelihood for the SAEM method. 
AIC 
Akaike information criterion. 
BIC 
Bayesian information criterion. 
Iterations 
number of iterations needed to converge. 
ptime 
processing time. 
range 
the effective range. 
The SAEM final estimates correspond to the estimates obtained at the last iteration of the algorithm.
To fit a regression model for noncensored data, just set cens
as a vector of zeros.
Functions print
, summary
, and plot
work for objects of class sclm
.
Katherine L. Valeriano, Alejandro Ordonez, Christian E. Galarza and Larissa A. Matos.
EM.sclm
, MCEM.sclm
, predict.sclm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  # Simulated example: 10% of rightcensored observations
n = 50 # Test with another values for n
set.seed(1000)
coords = round(matrix(runif(2*n,0,15),n,2),5)
x = cbind(rbinom(n,1,0.50), rnorm(n), rnorm(n))
data = rCensSp(c(1,4,2),2,3,0.50,x,coords,"right",0.10,0,"matern",2)
fit = SAEM.sclm(y=data$yobs, x=data[,7:9], cens=data$cens, LI=data$LI,
LS=data$LS, coords=data[,5:6], init.phi=2, init.nugget=1,
type="matern", kappa=2, MaxIter = 20, error=1e4)
summary(fit)
# Simulated example: censored and missing observations
n = 200
set.seed(123)
coords = round(matrix(runif(2*n,0,20),n,2),5)
x = cbind(1, rnorm(n), rexp(n))
data = rCensSp(c(1,4,1),2,4,0.50,x,coords,"left",0.10,0,"exponential",0)
data$yobs[c(10,20)] = NA; data$cens[c(10,20)] = 1
data$LI[c(10,20)] = Inf; data$LS[c(10,20)] = Inf
fit2 = SAEM.sclm(y=data$yobs, x=data[,7:9], cens=data$cens, LI=data$LI,
LS=data$LS, coords=data[,5:6], init.phi=2, init.nugget=1,
type="exponential", MaxIter = 300, error=1e4)
fit2$theta # Estimates
fit2$SE # Standard error
fit2$InfMat # Information matrix
plot(fit2)

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.