maxim.integrand {RiskMap}

Maximization of the Integrand for Generalized Linear Gaussian Process Models

Description

Maximizes the integrand function for Generalized Linear Gaussian Process Models (GLGPMs), which involves the evaluation of likelihood functions with spatially correlated random effects.

Usage

maxim.integrand(
  y,
  units_m,
  mu,
  Sigma,
  ID_coords,
  ID_re = NULL,
  family,
  sigma2_re = NULL,
  hessian = FALSE,
  gradient = FALSE
)

Arguments

y

Response variable vector.

units_m

Units of measurement for the response variable.

mu

Mean vector of the response variable.

Sigma

Covariance matrix of the spatial process.

ID_coords

Indices mapping response to locations.

ID_re

Indices mapping response to unstructured random effects.

family

Distribution family for the response variable. Must be one of 'gaussian', 'binomial', or 'poisson'.

sigma2_re

Variance of the unstructured random effects.

hessian

Logical; if TRUE, compute the Hessian matrix.

gradient

Logical; if TRUE, compute the gradient vector.

Details

This function maximizes the integrand for GLGPMs using the Nelder-Mead optimization algorithm. It computes the likelihood function incorporating spatial covariance and unstructured random effects, if provided.

The integrand includes terms for the spatial process (Sigma), unstructured random effects (sigma2_re), and the likelihood function (llik) based on the specified distribution family ('gaussian', 'binomial', or 'poisson').

Value

A list containing the mode estimate, and optionally, the Hessian matrix and gradient vector.

Author(s)

Emanuele Giorgi [e-mail]

Claudio Fronterre [e-mail]