Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/EstEMspatial_USER.R
This function returns the maximum likelihood (ML) estimates of the unknown parameters in Gaussian spatial models with censored/missing responses via the EM 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 
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 EM algorithm. 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 EM algorithm initially proposed by
\insertCitedempster1977maximum;textualRcppCensSpatial. The conditional expectations are
computed through function meanvarTMD
available in package MomTrunc
\insertCitegalarza2019momentsRcppCensSpatial.
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 
first moment for the truncated normal distribution computed in the last iteration. 
EYY 
second moment for the truncated normal distribution computed in the last iteration. 
SE 
vector of standard errors of θ = (β, σ^2, φ, τ^2). 
InfMat 
observed information matrix. 
loglik 
loglikelihood for the EM method. 
AIC 
Akaike information criterion. 
BIC 
Bayesian information criterion. 
Iterations 
number of iterations needed to converge. 
ptime 
processing time. 
range 
the effective range. 
The EM final estimates correspond to the estimates obtained at the last iteration of the EM 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.
SAEM.sclm
, MCEM.sclm
, predict.sclm
1 2 3 4 5 6 7 8 9 10 11  # Simulated example: 10% of leftcensored 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(rnorm(n), runif(n))
data = rCensSp(c(1,3),2,4,0.5,x,coords,"left",0.10,0,"gaussian",0)
fit = EM.sclm(y=data$yobs, x=data[,7:8], cens=data$cens, LI=data$LI,
LS=data$LS, coords=data[,5:6], init.phi=3, init.nugget=1,
type="gaussian", error=1e4)
fit

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