mgwrsar (version 1.3.1)

simu_multiscale: Simulate Data Generating Processes (DGP) for Multiscale GWR

Description

The simu_multiscale function generates synthetic datasets with spatially varying coefficients based on Data Generating Processes (DGP) proposed in the literature. It supports formulations from Fotheringham et al. (2017), Gao et al. (2021), and Geniaux (2024). It also allows for the introduction of spatial autocorrelation (SAR) in the response variable.

Usage

simu_multiscale(
  n = 1000,
  myseed = 1,
  type = "GG2024",
  constant = NULL,
  nuls = NULL,
  lambda = NULL,
  NN = 4,
  config_beta = "default",
  config_snr = 0.7,
  config_eps = "normal"
)

Value

A named list containing:

mydata

A data frame with the simulated response variable y and explanatory variables.

coords

A matrix of spatial coordinates.

Betav

A matrix of the true spatially varying coefficients.

W

The spatial weight matrix (if lambda is not NULL).

Arguments

n

Integer. The number of observations to simulate. Default is 1000.

myseed

Integer. Random seed for reproducibility. Default is 1.

type

Character. The type of DGP to use. Options are 'FT2017', 'Gao2021', or 'GG2024' (default).

constant

Vector. Indices or names of explanatory variables that should have constant (spatially stationary) coefficients. Default is NULL (all coefficients vary).

nuls

Vector. Indices of explanatory variables that should have a null effect (coefficient = 0). Default is NULL.

lambda

Numeric. The spatial autoregressive parameter (rho) if a SAR process is desired. Default is NULL (no spatial autocorrelation).

NN

Integer. The number of nearest neighbors used to construct the spatial weight matrix W if lambda is provided. Default is 4.

config_beta

Character. Configuration of the spatial pattern for Beta coefficients (e.g., 'default').

config_snr

Numeric. The desired Signal-to-Noise Ratio (SNR). Default is 0.7.

config_eps

Character. The distribution of the error term. Options are 'normal' (default), 'unif', or 'Chi2'.

References

Fotheringham, A. S., Yang, W., & Kang, W. (2017). Multiscale geographically weighted regression (MGWR). Annals of the American Association of Geographers, 107(6), 1247-1265.

Gao, S., Mei, C. L., Xu, Q. X., & Wang, N. (2021). Non-iterative multiscale estimation for spatial autoregressive geographically weighted regression models. Entropy, 25(2), 320.

Geniaux, G. (2025). Top-Down Scale Approaches for Multiscale GWR with Locally Adaptive Bandwidths. Springer Nature, 2021 LATEX template.

Examples

# \donttest{
 library(mgwrsar)
 library(ggplot2)
 library(gridExtra)
 library(grid)

 # Simulate data using Geniaux (2024) DGP
 simu <- simu_multiscale(n = 1000, type = 'GG2024', config_snr = 0.7)
 mydata <- simu$mydata
 coords <- simu$coords

 # Visualizing the spatial patterns of the coefficients
 p1 <- ggplot(mydata, aes(x, y, col = Beta1)) + geom_point() + scale_color_viridis_c()
 p2 <- ggplot(mydata, aes(x, y, col = Beta2)) + geom_point() + scale_color_viridis_c()
 p3 <- ggplot(mydata, aes(x, y, col = Beta3)) + geom_point() + scale_color_viridis_c()
 p4 <- ggplot(mydata, aes(x, y, col = Beta4)) + geom_point() + scale_color_viridis_c()

 grid.arrange(p1, p2, p3, p4, nrow = 2, ncol = 2,
              top = textGrob("DGP Geniaux (2024)", gp = gpar(fontsize = 20, font = 3)))
# }