MCEM.sclm: ML estimation of spatial censored linear models via the MCEM...

In RcppCensSpatial: Spatial Estimation and Prediction for Censored/Missing Responses

ML estimation of spatial censored linear models via the MCEM algorithm

Description

It fits the left, right, or interval spatial censored linear model using the Monte Carlo EM (MCEM) algorithm. It provides estimates and standard errors of the parameters and supports missing values on the dependent variable.

Usage

MCEM.sclm(y, x, ci, lcl = NULL, ucl = NULL, coords, phi0, nugget0,
  type = "exponential", kappa = NULL, lower = c(0.01, 0.01),
  upper = c(30, 30), MaxIter = 500, nMin = 20, nMax = 5000,
  error = 1e-04, show_se = TRUE)

Arguments

y	vector of responses of length n.
x	design matrix of dimensions n\times q, where q is the number of fixed effects, including the intercept.
ci	vector of censoring indicators of length n. For each observation: 1 if censored/missing, 0 otherwise.
lcl, ucl	vectors of length n representing the lower and upper bounds of the interval, which contains the true value of the censored observation. Default =NULL, indicating no-censored data. For each observation: lcl=-Inf and ucl=c (left censoring); lcl=c and ucl=Inf (right censoring); and lcl and ucl must be finite for interval censoring. Moreover, missing data could be defined by setting lcl=-Inf and ucl=Inf.
coords	2D spatial coordinates of dimensions n\times 2.
phi0	initial value for the spatial scaling parameter.
nugget0	initial value for the nugget effect parameter.
type	type of spatial correlation function: 'exponential', 'gaussian', 'matern', and 'pow.exp' for exponential, gaussian, matérn, and power exponential, respectively.
kappa	parameter for some spatial correlation functions. See CovMat.
lower, upper	vectors of lower and upper bounds for the optimization method. If unspecified, the default is c(0.01,0.01) for lower and c(30,30) for upper.
MaxIter	maximum number of iterations for the MCEM algorithm. By default =500.
nMin	initial sample size for Monte Carlo integration. By default =20.
nMax	maximum sample size for Monte Carlo integration. By default =5000.
error	maximum convergence error. By default =1e-4.
show_se	logical. It indicates if the standard errors should be estimated by default =TRUE.

Details

The spatial Gaussian model is given by

Y = Xβ + ξ,

where Y is the n\times 1 response vector, X is the n\times q design matrix, β is the q\times 1 vector of regression coefficients to be estimated, and ξ is the error term. Which is normally distributed with zero-mean and covariance matrix Σ=σ^2 R(φ) + τ^2 I_n. We assume that Σ is non-singular and X has a full rank \insertCitediggle2007springerRcppCensSpatial.

The estimation process is performed via the MCEM algorithm, initially proposed by \insertCitewei1990monte;textualRcppCensSpatial. The Monte Carlo (MC) approximation starts with a sample of size nMin; at each iteration, the sample size increases (nMax-nMin)/MaxIter, and at the last iteration, the sample size is nMax. The random observations are sampled through the slice sampling algorithm available in package relliptical.

Value

An object of class "sclm". Generic functions print and summary have methods to show the results of the fit. The function plot can extract convergence graphs for the parameter estimates.

Specifically, the following components are returned:

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	MC approximation of the first conditional moment.
EYY	MC approximation of the second conditional moment.
SE	vector of standard errors of θ = (β, σ^2, φ, τ^2).
InfMat	observed information matrix.
loglik	log-likelihood for the MCEM method.
AIC	Akaike information criterion.
BIC	Bayesian information criterion.
Iter	number of iterations needed to converge.
time	processing time.
call	RcppCensSpatial call that produced the object.
tab	table of estimates.
critFin	selection criteria.
range	effective range.
ncens	number of censored/missing observations.
MaxIter	maximum number of iterations for the MCEM algorithm.

Note

The MCEM final estimates correspond to the mean of the estimates obtained at each iteration after deleting the half and applying a thinning of 3.

To fit a regression model for non-censored data, just set ci as a vector of zeros.

Author(s)

Katherine L. Valeriano, Alejandro Ordoñez, Christian E. Galarza, and Larissa A. Matos.

References

\insertAllCited

See Also

EM.sclm, SAEM.sclm, predict.sclm

Examples

# Example 1: left censoring data
set.seed(1000)
n = 50   # Test with another values for n
coords = round(matrix(runif(2*n,0,15),n,2), 5)
x = cbind(rnorm(n), rnorm(n))
data = rCensSp(c(2,-1), 2, 3, 0.70, x, coords, "left", 0.08, 0, "matern", 1)

fit = MCEM.sclm(y=data$y, x=x, ci=data$ci, lcl=data$lcl, ucl=data$ucl,
                coords, phi0=2.50, nugget0=0.75, type="matern",
                kappa=1, MaxIter=30, nMax=1000)
fit$tab

# Example 2: left censoring and missing data
yMiss = data$y
yMiss[20] = NA
ci = data$ci
ci[20] = 1
ucl = data$ucl
ucl[20] = Inf

fit1 = MCEM.sclm(y=yMiss, x=x, ci=ci, lcl=data$lcl, ucl=ucl, coords,
                 phi0=2.50, nugget0=0.75, type="matern", kappa=1,
                 MaxIter=300, nMax=1000)
summary(fit1)
plot(fit1)

RcppCensSpatial documentation built on June 28, 2022, 1:07 a.m.