algnaive12: Naive 1 and Naive 2 method for spatial prediction. In CensSpatial: Censored Spatial Models

Description

This function performs spatial censored estimation and prediction for left and right censure through the Naive 1 and Naive 2 methods.

Usage

 ```1 2``` ```algnaive12(data, cc, copred, thetaini, y.col = 3,coords.col = 1:2,covar=F, covar.col, fix.nugget = T, nugget, kappa = 0, cov.model = "exponential", trend) ```

Arguments

 `data` data.frame containing the coordinates, covariates and the response variable (in any order). `cc` (binary vector) indicator of censure (1: censored observation 0: observed). `copred` coordinates used in the prediction procedure. `thetaini` initial values for the σ^2 and φ values in the covariance structure. `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. `fix.nugget` (logical) it indicates if the τ^2 parameter must be fixed. `nugget` (numeric) values of the τ^2 parameter, if `fix.nugget=F` this value corresponds to an initial value. `kappa` value of κ used in some covariance functions. `cov.model` structure of covariance (see `cov.spatial` from `geoR`). `trend` it specifies the mean part of the model. See documentation of trend.spatial from geoR for further details. By default it takes `"cte"`.

Details

The Naive 1 and Naive 2 are computed as in Schelin (2014). The naive 1 replaces the censored observations by the limit of detection (LD) and it performs estimation and prediction with this data. Instead of 1, the naive 2 replaces the censored observations by LD/2.

Value

 `beta1` beta parameter for the mean structure in the Naive 1 method. `beta2` beta parameter for the mean structure in the Naive 2 method. `theta1` vector of estimate parameter for the mean and covariance structure (β, σ^2, φ, τ^2) in the Naive 1 method. `theta2` vector of estimate parameter for the mean and covariance structure (β, σ^2, φ, τ^2) in the Naive 2 method. `predictions1` predictions obtained for the Naive 1 method. `predictions2` predictions obtained for the Naive 2 method. `AIC1` AIC of the estimated model in the Naive 1 method. `AIC2` AIC of the estimated model in the Naive 2 method. `BIC1` BIC of the estimated model in the Naive 1 method. `BIC2` BIC of the estimated model in the Naive 2 method. `loglik1` log likelihood for the estimated model in the Naive 1 method. `loglik2` log likelihood for the estimated model in the Naive 2 method. `sdpred1` standard deviations of predictions in the Naive 1 method. `sdpred2` standard deviations of predictions in the Naive 2 method.

Author(s)

Alejandro Ordonez <<[email protected]>>, Victor H. Lachos <<[email protected]>> and Christian E. Galarza <<[email protected]>>

Maintainer: Alejandro Ordonez <<[email protected]>>

References

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

`SAEMSCL`
 ``` 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 30 31 32 33 34 35 36 37``` ```## Not run: n<-200 ### sample size for estimation. n1=100 ### number of observation used for prediction. ###simulated coordinates 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] aux2=algnaive12(data=data2,cc=obj\$cc,covar=T,covar.col=4:5, copred=obj\$coords1,thetaini=c(.1,.2),y.col=3,coords.col=1:2, fix.nugget=T,nugget=0,kappa=1.2,trend=~V4+V5,cov.model=type) ## End(Not run) ```