spatemR (version 1.2.0)

SARARgamlss: SARARgamlss: Spatial Autoregressive Generalized Additive Model for Location Scale (GAMLSS)

Description

This function estimates a Spatial Autoregressive Generalized Additive Model for Location Scale (SARARgamlss) using GAMLSS. The model includes both spatial dependencies and the possibility of non-parametric terms in the formulas for the mean and variance. The function supports SAR, SARAR, and SEM model types and performs the estimation through an iterative process that updates spatial dependence parameters. The variance of the spatial parameters \(\hat{\rho}\) and \(\hat{\lambda}\) is estimated using the inverse of the Hessian matrix from the optimization.

Usage

SARARgamlss(
  formula,
  sigma.formula = ~1,
  W1 = diag(0, nrow(data)),
  W2 = diag(0, nrow(data)),
  data,
  tol = 1e-04,
  maxiter = 20,
  type = c("SAR", "SARAR", "SEM"),
  weights = NULL
)

Value

A fitted GAMLSS model object with spatial autoregressive terms. The model object also includes the variance of the spatial parameters \(\hat{\rho}\) and \(\hat{\lambda}\)

Arguments

formula

A formula specifying the mean structure of the model (response ~ explanatory variables).

sigma.formula

A formula specifying the variance structure of the model (default: ~1).

W1

A spatial weights matrix for the SAR term (default: identity matrix).

W2

A spatial weights matrix for the SARAR term (default: identity matrix).

data

A data.frame containing the variables used in the model.

tol

Convergence tolerance (default: 1E-4).

maxiter

Maximum number of iterations for optimization (default: 20).

type

The type of spatial model to fit: one of "SAR", "SARAR", or "SEM".

weights

Optional weights for the observations (default: NULL).

References

Toloza-Delgado, J. D., Melo, O. O., & Cruz, N. A. Joint spatial modeling of mean and non-homogeneous variance combining semiparametric SAR and GAMLSS models for hedonic prices. Spatial Statistics, 65, 100864 (2025) @source https://doi.org/10.1016/j.spasta.2024.100864

Examples

library(spdep)
library(gamlss)
data(oldcol)
# Create spatial weight matrices W1 and W2
W1 <- spdep::nb2mat(COL.nb, style = "W")
W2 <- W1  # In this case, assume the same spatial weights for both
# Fit a SARARgamlss model
result <- SARARgamlss(formula = CRIME ~ INC + cs(HOVAL), 
sigma.formula = ~ INC + pb(HOVAL), W1 = W1, W2 = W2,data = COL.OLD, 
tol = 1E-4,  maxiter = 20, type = "SARAR")
summary_SAR(result)
gamlss::term.plot(result$gamlss, what="mu")