rGClat {SpatGC}

Generate Data from GC Spatial Regression Model with Lattice Spatial Effect

Description

This function generates spatially dependent count data based on the Gamma-Count (GC) spatial regression model. It uses a specified spatial dependency model (either ICAR or CAR) and optional adjacency matrix or shapefile for spatial relationships. The function returns a list containing the generated data and relevant information about the simulation.

Usage

rGClat(
  n = n,
  alpha,
  beta0,
  beta,
  spatial = "ICAR",
  W = NULL,
  V = NULL,
  rho = 1,
  shapefile = NULL
)

Arguments

n

Integer. The number of knots (or spatial units) for which the data should be generated. If a shapefile or adjacency matrix ('W') is provided, this will be determined from those inputs.

alpha

Numeric. The dispersion parameter of the Gamma-Count model.

beta0

Numeric. The intercept term for the model.

beta

Numeric vector. The regression coefficients (fixed effects) for the model.

spatial

Character. Specifies the type of spatial dependency to use. Options are "ICAR" for Intrinsic Conditional Autoregressive, or "CAR" for Conditional Autoregressive.

W

Optional matrix. The adjacency matrix for lattice data. If provided, it will be used to define spatial relationships between knots.

V

Optional numeric. The variance of the spatial random effects for lattice data.

rho

Optional numeric. The spatial correlation coefficient for the CAR model. Default is 1.

shapefile

Optional. A shapefile defining the spatial relationships between knots. If provided, it will be used to define an adjacency matrix.

Value

A list containing the following components:

covariate

A matrix of covariates with the specified number of knots ('n') and columns based on the length of 'beta'.

phi

A vector of spatial random effects, generated based on the specified spatial dependency model ('spatial').

eta

A vector representing the linear predictor, calculated as the dot product of the covariates and coefficients plus the spatial effects ('phi').

y

A vector of simulated count data based on the GC model and the linear predictor ('eta').

ID

A vector of knot IDs from 1 to 'n'.

Examples

# Generate a random adjacency matrix for a 429x429 grid
W <- rAdj(429)

# Generate data from the GC spatial regression model with the specified parameters
data <- rGClat(n = 200, alpha = 1, beta0 = 0.3, beta = c(-0.5, 0.5),
spatial = "ICAR", W = W, V = 1)

# View the generated data
print(data)