multiscale_gwr: Multiscale Geographically Weighted Regression (MGWR)

Description

This function estimates a Multiscale Geographically Weighted Regression (MGWR) model based on the proposition of Fotheringham et al. (2017). Unlike standard GWR where a single bandwidth is used for all covariates, MGWR allows for covariate-specific bandwidths. It uses a backfitting algorithm to iteratively estimate the optimal bandwidth and coefficients for each explanatory variable.

Usage

multiscale_gwr(formula, data, coords, kernels = 'bisq',
                      control_mgwr = list(), control = list())

Value

An object of class mgwrsar containing:

Betav: Matrix of estimated spatially varying coefficients.
H: Vector of final optimal bandwidths for each covariate.
RMSE: Root Mean Square Error of the final model.
residuals: Vector of residuals.
fitted.values: Vector of fitted values.
AICc: Corrected AIC (if get_AIC = TRUE).
R2: R-squared of the model.

Arguments

formula: A formula object specifying the model (e.g., y ~ x1 + x2).
data: A data frame containing the variables in the model.
coords: A matrix or data frame of coordinates (2 columns for spatial, 3 for spatio-temporal).
kernels: A character string specifying the kernel type. Options include 'bisq' (default), 'gauss', 'triangle', 'tricube', 'rectangle'.
control_mgwr: A named list of control parameters specific to the MGWR backfitting algorithm. See 'Details' for available components.
control: A named list of standard control arguments passed to the internal GWR estimation steps. See 'Details' for available components.

Details

Components for control_mgwr:

init: Character. The type of model used for initialization. Options are 'GWR' (default) or 'lm' (OLS).
maxiter: Integer. Maximum number of backfitting iterations. Default is 20.
tolerance: Numeric. Convergence threshold based on the change in RMSE or bandwidths. Default is 1e-6.
nstable: Integer. Number of consecutive iterations where bandwidths must remain stable to declare convergence. Default is 6.
H0: Numeric vector. Optional initial bandwidths for each covariate. If NULL, they are initialized via GWR or global search.
get_AIC: Logical. If TRUE, calculates the corrected Akaike Information Criterion (AICc) at the end. Default is FALSE.
verbose: Logical. If TRUE, prints progress information during backfitting. Default is FALSE.

Components for control:

adaptive: Logical. If TRUE (default), uses an adaptive bandwidth (k-nearest neighbors). If FALSE, uses a fixed distance bandwidth.
Type: Character. The type of spatial weighting. 'GD' (Geographical Distance, default) or 'GDT' (Geo-Temporal).
NN: Integer. Maximum number of neighbors for matrix truncation (speeds up computation). Default is nrow(data).
ncore: Integer. Number of cores to use for parallel computation.
isgcv: Logical. If TRUE, computes Leave-One-Out Cross-Validation scores. Default is FALSE.

References