GEESAR: Generalized Estimating Equations with Spatial Autoregressive...

In spatemR: Generalized Spatial Autoregresive Models for Mean and Variance

Generalized Estimating Equations with Spatial Autoregressive Components

Description

'GEESAR' estimates generalized estimating equations (GEE) incorporating spatial autoregressive (SAR) components. It extends GEE models to account for spatial dependence in the response variable.

Usage

GEESAR(
  formula,
  family = gaussian(),
  weights = NULL,
  data,
  W,
  start = NULL,
  toler = 1e-04,
  maxit = 200,
  trace = FALSE
)

Arguments

formula	A formula specifying the model structure (response ~ predictors).
family	A description of the error distribution and link function. Default is 'gaussian()'.
weights	Optional vector of prior weights. Must be positive.
data	A data frame containing the variables in the model.
W	A spatial weights matrix defining the spatial dependence structure.
start	Optional starting values for parameter estimation.
toler	Convergence tolerance for iterative optimization. Default is '1e-05'.
maxit	Maximum number of iterations for model fitting. Default is '50'.
trace	Logical; if 'TRUE', prints iteration details. Default is 'FALSE'.

Details

The function estimates a spatially autoregressive GEE model by iteratively updating the spatial dependence parameter ('rho') and regression coefficients ('beta'). The estimation follows a quasi-likelihood approach using iterative weighted least squares (IWLS).

The function supports common GLM families ('gaussian', 'binomial', 'poisson', 'Gamma', 'inverse.gaussian') and their quasi-likelihood equivalents.

Value

A list of class '"GEESAR"' containing:

coefficients	Estimated regression coefficients.
rho	Estimated spatial autoregressive parameter.
fitted.values	Predicted values from the model.
linear.predictors	Linear predictor values ('X * beta').
prior.weights	Weights used in estimation.
y	Observed response values.
formula	Model formula.
call	Function call used to fit the model.
data	Data used in the model.
converged	Logical indicating whether the algorithm converged.
logLik	Quasi-log-likelihood of the fitted model.
deviance	Residual deviance.
df.residual	Residual degrees of freedom.
phi	Dispersion parameter estimate.
CIC	Corrected Information Criterion.
RJC	Robust Jackknife Correction.

Source

https://doi.org/10.48550/arXiv.2412.00945

References

Cruz, N. A., Toloza-Delgado, J. D., & Melo, O. O. (2024). Generalized spatial autoregressive model. arXiv preprint arXiv:2412.00945.

See Also

glm, gee, spdep

Examples

library(spdep)
library(sp)
data(meuse)
sp::coordinates(meuse) <- ~x+y
W <- spdep::nb2mat(knn2nb(knearneigh(meuse, k=5)), style="W")
fit <- GEESAR(cadmium ~ dist + elev, family=poisson(), data=meuse, W=W)
summary_SAR(fit)

spatemR documentation built on June 8, 2025, 1:16 p.m.