Seminaive {CensSpatial}

Seminaive algorithm for spatial censored prediction.

Description

This function executes the seminaive algorithm proposed by Schelin et al. (2014)

Usage

Seminaive(data, y.col, coords.col, covar, covar.col, copred,cov.model = "exponential",
thetaini, fix.nugget = TRUE, nugget,kappa = 0, cons, MaxIter, cc, cutoff, trend)

Arguments

data

data.frame containing the coordinates, covariates and response variable.

y.col

(numeric) column of data.frame that corresponds to the response variable.

coords.col

(numeric) columns of data.frame that corresponds to the coordinates of the spatial data.

covar

(logical) indicates the presence of covariates in the spatial censored estimation (FALSE: without covariates, TRUE: with covariates).

covar.col

(numeric) columns of data.frame that corresponds to the covariates in the spatial censored linear model estimation.

copred

coordinates used in the prediction procedure.

cov.model

covariance model in the structure of covariance (see cov.spatial from geoR).

thetaini

initial values for the \sigma^2 and \phi values in the covariance structure.

fix.nugget

(logical) it indicates if the \tau^2 parameter must be fixed.

nugget

(numeric) values of the \tau^2 parameter, if fix.nugget=F, this value corresponds to an initial value.

kappa

value of \kappa involved in some covariance functions.

cons

(vector) vector containing the (c_1,c_2,c_3) constants used in the convergence criterion for the algorithm (see Schedlin).

MaxIter

maximum of iterations for the algorithm.

cc

(binary vector) indicator of censure (1: censored, 0: observed)

cutoff

(vector) limit of detection for censure ( rc: >cutoff, lc: <cutoff)

trend

it specifies the mean part of the model. See documentation of trend.spatial from geoR for further details. By default "cte".

Details

This function estimates and computes predictions following Schedlin et al. (2014). See reference.

Value

zk

vector with observed and estimate censored observations by kriging prediction.

AIC

AIC of the estimated model.

BIC

BIC of the estimated model.

beta

beta parameter for the mean structure.

theta

vector of estimate parameters for the mean and covariance structure (\beta,\sigma^2,\phi,\tau^2).

predictions

Predictions obtained for the seminaive algorithm.

sdpred

Standard deviations of predictions.

loglik

log likelihood from the estimated model.

Author(s)

Alejandro Ordonez <<[e-mail]>>, Victor H. Lachos <<[e-mail]>> and Christian E. Galarza <<[e-mail]>>

Maintainer: Alejandro Ordonez <<[e-mail]>>

References

Schelin, L. & Sjostedt-de Luna, S. (2014). Spatial prediction in the presence of left-censoring. Computational Statistics and Data Analysis, 74.

See Also

SAEMSCL

Examples

n<-200 ### sample size for estimation.
n1=100 ### number of observation used in the prediction.

###simulated coordinates.
r1=sample(seq(1,30,length=400),n+n1)
r2=sample(seq(1,30,length=400),n+n1)
coords=cbind(r1,r2)### total coordinates (used in estimation and prediction).
coords1=coords[1:n,]####coordinates used for estimation.

type="matern"### covariance structure.

xtot<-cbind(1,runif((n+n1)),runif((n+n1),2,3))## X matrix for estimation and prediction.
xobs=xtot[1:n,]## X matrix for estimation.

###simulated data.
obj=rspacens(cov.pars=c(3,.3,0),beta=c(5,3,1),x=xtot,coords=coords,kappa=1.2,
cens=0.25,n=(n+n1),n1=n1,cov.model=type,cens.type="left")

data2=obj$datare
data2[,4:5]=xobs[,-1]

cc=obj$cc
y=obj$datare[,3]
cutoff=rep(obj$cutoff,length(y[cc==1]))

###seminaive algorithm
r=Seminaive(data=data2,y.col=3,covar=TRUE,coords.col=1:2,covar.col=4:5,cov.model="matern",
thetaini=c(.1,.2),fix.nugget=TRUE,nugget=0,kappa=1.5,cons=c(0.1,2,0.5),MaxIter=100,
cc=obj$cc,cutoff=cutoff,copred=obj$coords1,trend=~V4+V5)

summary(r)