likfit.glsm: Monte Carlo Maximum Likelihood Estimation in a Generalised...
In geoRglm: A Package for Generalised Linear Spatial Models

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

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

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, ...)

`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`.

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.

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.

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

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.

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.

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)