Simulation from Generalized Linear Gaussian Process Models
glgpm_sim.RdSimulates data from a fitted Generalized Linear Gaussian Process Model (GLGPM) or a specified model formula and data.
Usage
glgpm_sim(
n_sim,
model_fit = NULL,
formula = NULL,
data = NULL,
family = NULL,
den = NULL,
cov_offset = NULL,
crs = NULL,
convert_to_crs = NULL,
scale_to_km = TRUE,
sim_pars = list(beta = NULL, sigma2 = NULL, tau2 = NULL, phi = NULL, sigma2_me = NULL,
sigma2_re = NULL),
messages = TRUE
)Arguments
- n_sim
Number of simulations to perform.
- model_fit
Fitted GLGPM model object of class 'RiskMap'. If provided, overrides 'formula', 'data', 'family', 'crs', 'convert_to_crs', 'scale_to_km', and 'control_mcmc' arguments.
- formula
Model formula indicating the variables of the model to be simulated.
- data
Data frame or 'sf' object containing the variables in the model formula.
- family
Distribution family for the response variable. Must be one of 'gaussian', 'binomial', or 'poisson'.
- den
Required for 'binomial' to denote the denominator (i.e. number of trials) of the Binomial distribution. For the 'poisson' family, the argument is optional and is used a multiplicative term to express the mean counts.
- cov_offset
Offset for the covariate part of the GLGPM.
- crs
Coordinate reference system (CRS) code for spatial data.
- convert_to_crs
CRS code to convert spatial data if different from 'crs'.
- scale_to_km
Logical; if TRUE, distances between locations are computed in kilometers; if FALSE, in meters.
- sim_pars
List of simulation parameters including 'beta', 'sigma2', 'tau2', 'phi', 'sigma2_me', and 'sigma2_re'.
- messages
Logical; if TRUE, display progress and informative messages.
Value
A list containing simulated data, simulated spatial random effects (if applicable), and other simulation parameters.
Details
Generalized Linear Gaussian Process Models (GLGPMs) extend generalized linear models (GLMs) by incorporating spatial Gaussian processes to model spatial correlation. This function simulates data from GLGPMs using Markov Chain Monte Carlo (MCMC) methods. It supports Gaussian, binomial, and Poisson response families, utilizing a Matern correlation function to model spatial dependence.
The simulation process involves generating spatially correlated random effects and simulating responses based on the fitted or specified model parameters. For 'gaussian' family, the function simulates response values by adding measurement error.
Additionally, GLGPMs can incorporate unstructured random effects specified through the re() term in the model formula, allowing for capturing additional variability beyond fixed and spatial covariate effects.