spatemR (version 1.2.0)

GEESAR: 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
)

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.

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.

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

# \donttest{
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)
# }