spatCAR {SpatGC}

Generate Spatial Random Fields from CAR Models

Description

This function generates spatial random fields from Conditional Autoregressive (CAR) models for lattice spatial data. Given a neighborhood matrix, a variance parameter, and a spatial dependence parameter, the function produces a spatial random field.

Usage

spatCAR(W, sig, rho)

Arguments

W

Numeric matrix. The neighborhood matrix representing the adjacency relationships between spatial units. It can be provided by using the function 'rAdj'.

sig

Numeric. The variance of the spatial random effects from the CAR model. Must be positive.

rho

Numeric. The spatial dependence parameter for the CAR model. Must be between -1 and 1, inclusive.

Details

The function starts by computing the diagonal matrix of the number of neighbors for each spatial unit. Then, it calculates the precision matrix (Q) based on the given parameters and neighborhood matrix. A small constant (0.0001) is added to the diagonal to ensure the precision matrix is non-singular. Finally, the covariance matrix is calculated as the inverse of the precision matrix multiplied by the variance parameter ('sig'). The function uses multivariate normal random generation (using 'rmvnorm' from the 'mvtnorm' package) to produce the spatial random field.

Value

A numeric vector representing the spatial random field from the CAR model. The length of the vector is equal to the number of spatial units (rows in the neighborhood matrix).

Examples

# Generate a random adjacency matrix for 5 spatial regions with a probability of 0.2
W <- rAdj(n = 5, p = 0.2)

# Generate a spatial random field from the CAR model using the adjacency matrix
# with parameters variance = 0.1, and rho = 0.5
spatial_random_field <- spatCAR(W = W, sig = 0.1, rho = 0.5)
print(spatial_random_field)