Poislat {SpatGC}

Fit Poisson Spatial Model

Description

This function fits a Poisson spatial model (including zero-inflated and gamma Poisson variations) to a given dataset using the INLA package. It constructs the formula based on the provided covariate data and ID variables, and fits the model using the specified adjacency matrix ('W') or a shapefile of the study region.

Usage

Poislat(
  Y,
  ID,
  W = NULL,
  shapefile = NULL,
  covariate = NULL,
  family = c("gpoisson", "poisson", "zeroinflatedpoisson0", "zeroinflatedpoisson1")
)

Arguments

Y

Vector of response variables (counts).

ID

Vector of indexes of regions (spatial units).

W

Optional adjacency matrix representing spatial connections between regions. If not provided, it can be generated from a shapefile using the 'shapefile' argument.

shapefile

Optional shapefile representing the study region. If provided, the adjacency matrix ('W') will be calculated from the shapefile.

covariate

Optional matrix of covariates. If not provided, the function assumes the model is intercept-only.

family

The family of Poisson models to use. Options are "gpoisson", "poisson", "zeroinflatedpoisson0", and "zeroinflatedpoisson1".

Value

An object of class "inla" representing the fitted Poisson spatial model. The object contains model estimates, diagnostics, and other results.

Examples

  # Generate data from the GC spatial regression model with lattice spatial dependency
  W <- rAdj(500) # Generate a random adjacency matrix
  DDl <- rGClat(n = 200, alpha = 1, beta0 = 0.3, beta = c(-0.5, 0.5),
  W = W, spatial = "lattice", V = 1)

  # Prepare the data
  Y <- DDl$y
  covariate <- DDl$covariate
  ID <- DDl$ID

  # Fit the spatial Poisson model
  ResultPoisson <- Poislat(Y = Y, ID = ID, covariate = covariate, W = W, family = "poisson")

  # Summary of the model fit
  summary(ResultPoisson)