SDALGCPParaEst: SDALGCPParaEst function.

In olatunjijohnson/SDALGCP: Spatially Discrete Approximation to Log-Gaussian Cox Processes for Aggregated Disease Count Data

Description

This function provides the maximum likelihood estimation of the parameter given the precomputed correlation matrices for different values of scale parameter, phi. An internal function for SDALGCP package

Usage

SDALGCPParaEst(
  formula,
  data,
  corr,
  par0 = NULL,
  control.mcmc = NULL,
  plot_profile = FALSE,
  messages = FALSE
)

Arguments

formula	an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data	data frame containing the variables in the model.
corr	the array of the precomputed correlation matrix for each value of the scale parameter.
par0	the initial parameter of the fixed effects beta, the variance sigmasq and the scale parameter phi, specified as c(beta, sigma2, phi)
control.mcmc	list from PrevMap package to define the burnin, thining, the number of iteration and the turning parameters see controlmcmcSDA.
plot_profile	logical; if TRUE the profile-likelihood is plotted. default is FALSE
messages	logical; if message=TRUE, it prints the results objective function and the parameters at every phi iteration. Default is FALSE.

Details

This function performs parameter estimation for a SDALGCP Model Monte Carlo Maximum likelihood. The Monte Carlo maximum likelihood method uses conditional simulation from the distribution of the random effect T(x) = d(x)'β+S(x) given the data y, in order to approximate the high-dimensional intractable integral given by the likelihood function. The resulting approximation of the likelihood is then maximized by a numerical optimization algorithm which uses analytic expression for computation of the gradient vector and Hessian matrix. The functions used for numerical optimization are nlminb

Value

An object of class "SDALGCP". The function summary.SDALGCP is used to print a summary of the fitted model. The object is a list with the following components:

D: matrix of covariates.

y: the count, response observations.

m: offset

beta_opt: estimates of the fixed effects of the model.

sigma2_opt: estimates of the variance of the Gaussian process.

phi_opt: estimates of the scale parameter phi of the Gaussian process.

cov: covariance matrix of the MCML estimates.

Sigma_mat_opt : covariance matrix of the Gaussian process that corresponds to the optimal value

llike_val_opt: maximum value of the log-likelihood.

mu: mean of the linear predictor

all_para: the entire estimates for the different values of phi.

all_cov: the entire covariance matrix of the estimates for the different values of phi.

par0: the initial parameter of the fixed effects beta and the variance sigmasq used in the estimation

control.mcmc: the burnin, thining, the number of iteration and the turning parameters used see controlmcmcSDA.

S: the linear predictor given the initial parameter

call: the matched call.

Author(s)

Olatunji O. Johnson [e-mail]

Emanuele Giorgi [e-mail]

Peter J. Diggle [e-mail]

References

Giorgi, E., & Diggle, P. J. (2017). PrevMap: an R package for prevalence mapping. Journal of Statistical Software, 78(8), 1-29. doi:10.18637/jss.v078.i08.

Christensen, O. F. (2004). Monte Carlo maximum likelihood in model-based geostatistics. Journal of Computational and Graphical Statistics 13, 702-718.

See Also

Aggregated_poisson_log_MCML, Laplace.sampling

olatunjijohnson/SDALGCP documentation built on March 20, 2021, 4:24 a.m.