likfit.glsm: Monte Carlo Maximum Likelihood Estimation in a Generalised...

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

This function performs Monte Carlo maximum likelihood in a generalised linear spatial model, based on a Monte Carlo sample from the conditional distribution.

Usage

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likfit.glsm(mcmc.obj, trend = mcmc.obj$trend, cov.model = "matern", 
       kappa = 0.5, ini.phi, fix.nugget.rel = FALSE, nugget.rel = 0, 
       aniso.pars = NULL, fix.lambda = TRUE, lambda = NULL, 
       limits = pars.limits(), messages, ...)

Arguments

mcmc.obj

object with the Monte Carlo simulations and corresponding approximating density. This object should be an output from the function prepare.likfit.glsm.

trend

specifies the covariate values at the data locations. See documentation of trend.spatial for further details. Default is that the trend is the same as in the mcmc.obj object.

cov.model

a string specifying the model for the correlation function. For further details see documentation for cov.spatial.

kappa

additional smoothness parameter required by the following correlation functions: "matern", "powered.exponential", "gneiting.matern" and "cauchy".

ini.phi

initial value for the covariance parameter phi.

fix.nugget.rel

logical, saying whether the parameter tau_R^2 (relative nugget) should be regarded as fixed (fix.nugget.rel = TRUE) or should be estimated (fix.nugget.rel = FALSE). Default is fix.nugget.rel = FALSE.

nugget.rel

value of the relative nugget parameter. Regarded as a fixed value if fix.nugget.rel = TRUE, otherwise as the initial value for the maximization algorithm. Default is nugget.rel = 0.

aniso.pars

parameters for geometric anisotropy correction. If aniso.pars = NULL the correction will be the same as for the generated sample in mcmc.obj. Otherwise a two elements vector with values for the anisotropy parameters must be provided. Anisotropy correction consists of a transformation of the data and prediction coordinates performed by the function coords.aniso.

fix.lambda

logical, indicating whether the Box-Cox transformation parameter lambda should be regarded as fixed (fix.lambda = TRUE) or should be be estimated (fix.lambda = FALSE). Default is fix.lambda = TRUE.

lambda

value of parameter lambda in the Box-Cox class of link functions. Regarded as a fixed value if fix.lambda = TRUE, otherwise as the initial value for the minimization algorithm. Default is lambda = NULL, in which case the used link function will be the same as for the generated sample in mcmc.obj.

limits

values defining lower and upper limits for the model parameters used in the numerical minimization. The auxiliary function pars.limits is used to set the limits.

messages

logical. Indicates whether status messages should be printed on the screen (or output device) while the function is running.

...

additional parameters to be passed to the optimisation function. Typically arguments of the type control() which controls the behavior of the optimization algorithm. For further details, see the documentation for the minimization function optim.

Details

This function estimates the parameters in the Poisson/Binomial normal model, using a Monte Carlo approximation to the likelihood. Further details can be found in Christensen (2004).

Parameter estimation is done numerically using the R function optim with box-constraints, i.e. method="L-BFGS-B".

Lower and upper limits for parameter values can be specified using the function pars.limits(). For example, including limits = pars.limits(phi=c(0.01, 10)) in the function call will specify the limits for the parameter phi. Default values are used if the argument limits is not provided.

Only when the mcmc.obj object contains an object mu giving the intensity, is it possible to use other link functions than the link function used for the generated sample in mcmc.obj

We strongly recommend that the user does not provide self-made input objects for mcmc.obj, but only uses objects created by prepare.likfit.glsm. In case the user really wants to create his own objects, he should study the source code very carefully to understand how it works.

Summary and print methods for summarising and printing the output also exist.

Value

A list with the following components:

family

the error distribution (Poisson or Binomial).

link

the name of the link function.

cov.model

a string with the name of the correlation function.

beta

estimate of the parameter beta. This can be a scalar or vector depending on the covariates (trend) specified in the model.

cov.pars

a vector with the estimates of the parameters sigma^2 and phi, respectively.

nugget.rel

value of the relative nugget parameter tau_R^2. This is an estimate if fix.nugget.rel = FALSE, and otherwise a given fixed value.

kappa

value of the smoothness parameter. Valid only when the correlation function is one of: "matern", "powered.exponential", "cauchy" or "gneiting.matern".

lambda

values of the parameter for the Box-Cox class of link functions. A fixed value if fix.lambda = TRUE, otherwise the estimated value.

aniso.pars

values of the anisotropy parameters used.

trend

the trend

parameters.summary

a data-frame with all model parameters, their status (estimated or fixed) and values.

loglik

the value of the maximized likelihood.

npars

number of estimated parameters.

info.minimisation

results returned by the minimisation function.

call

the function call.

Author(s)

Ole F. Christensen OleF.Christensen@agrsci.dk,
Paulo J. Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br.

References

Christensen, O. F. (2004). Monte Carlo maximum likelihood in model-based geostatistics. Journal of computational and graphical statistics 13 702-718.

Further information about geoRglm can be found at:
http://gbi.agrsci.dk/~ofch/geoRglm.

See Also

prepare.likfit.glsm on how to prepare the object mcmc.obj, glsm.mcmc for MCMC simulation in generalised linear spatial model, and summary.likGLSM for summarising the output. See also likfit for parameter estimation in the Gaussian spatial model.

Examples

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data(p50)

## Not run: 
mcmc.5 <- mcmc.control(S.scale = 0.6, thin=20, n.iter=50000, burn.in=1000)
model.5 <- list(cov.pars=c(0.6, 0.1), beta=1, family="poisson")
outmcmc.5 <- glsm.mcmc(p50, model= model.5, mcmc.input = mcmc.5)     
mcmcobj.5 <- prepare.likfit.glsm(outmcmc.5)   
lik.5 <- likfit.glsm(mcmcobj.5, ini.phi = 0.1, fix.nugget.rel = TRUE)
print(lik.5)
summary(lik.5)
lik.5.sph.nugget <- likfit.glsm(mcmcobj.5, ini.phi = 1, 
                           cov.model = "spherical", nugget.rel = 0.385)
print(lik.5.sph.nugget)
summary(lik.5.sph.nugget)

## End(Not run)

geoRglm documentation built on May 2, 2019, 4:03 p.m.