Maximization of the Integrand for Generalized Linear Gaussian Process Models
maxim.integrand.RdMaximizes 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').