mgwrfit fits MGWR (Fotheringham, Yang and Kang 2017) by backfitting
from OLS (intercept prepended when X has no constant column, predictors
not centred) with covariate-specific bandwidths, fixed or re-selected at
each pass by golden-section minimisation of the one-covariate AICc
(mgwrbw), and tracks the covariate-specific hat matrices for inference
(Yu et al. 2020): standard errors, ENP, tr S, sigma^2 = RSS/(n - tr S)
and AICc. mgwrcof, mgwrres, mgwrstd, mgwrhat return its
coefficients, residuals, standard errors and hat diagonal; mgwrcv the
leave-one-out score sum (e_i/(1 - S_ii))^2; mgwrbk runs the
backfitting with fixed bandwidths; mgwraic, mgwrdg and mgwrsig the
AICc, diagnostic summary and error variance from ll, tr S and the
residuals; mgwrtst the Monte Carlo test of coefficient variability with
Philox permutations.
Usage
mgwrfit(
y,
X,
coords,
bandwidths = NULL,
kernel = "bisquare",
adaptive = FALSE,
threshold = 1e-10,
max_iter = 500
)
mgwrcof(y, X, coords, bws = NULL, kernel = "bisquare", adaptive = FALSE)
mgwrres(y, X, coords, bws = NULL, kernel = "bisquare", adaptive = FALSE)
mgwrstd(y, X, coords, bws = NULL, kernel = "bisquare", adaptive = FALSE)
mgwrhat(y, X, coords, bws = NULL, kernel = "bisquare", adaptive = FALSE)
mgwrcv(y, X, coords, bws = NULL, kernel = "bisquare", adaptive = FALSE)
mgwrbw(
y,
X,
coords,
kernel = "bisquare",
adaptive = FALSE,
threshold = 1e-08,
max_iter = 200
)
mgwrbk(
y,
X,
coords,
bandwidths,
max_iter = 10,
kernel = "bisquare",
adaptive = FALSE,
threshold = 1e-10
)
mgwraic(ll, tr_S, n)
mgwrdg(ll, tr_S, n, k = NULL, alpha = 0.05)
mgwrsig(resid, tr_S, n = NULL)
mgwrtst(
y,
X,
coords,
nsim = 9,
bandwidths = NULL,
seed = 0,
kernel = "bisquare",
adaptive = FALSE,
threshold = 1e-08,
max_iter = 500
)Arguments
- y
Response.
- X
Regressors.
- coords
Coordinates.
- bandwidths, bws
Per-covariate bandwidths (intercept first); NULL selects them.
- kernel
Kernel name (see
GWRKernelWeights).- adaptive
Adaptive bandwidths.
- threshold
Convergence threshold of the backfitting.
- max_iter
Maximum number of backfitting passes.
- ll
Gaussian log-likelihood.
- tr_S
Trace of the hat matrix.
- n
Number of observations.
- k
Number of covariates (for the corrected test level).
- alpha
Nominal level.
- resid
Residuals.
- nsim
Number of permutations.
- seed
Philox seed.
Value
mgwrfit a list with betas, se, fitted, residuals,
hat_diagonal, enp, trS, rss, sigma2, aicc, bandwidths,
iterations; the others the corresponding parts.
References
Fotheringham, A. S., Yang, W. and Kang, W. (2017). Multiscale geographically weighted regression (MGWR). Annals of the American Association of Geographers 107, 1247-1265. Yu, H., Fotheringham, A. S., Li, Z., Oshan, T., Kang, W. and Wolf, L. J. (2020). Inference in multiscale geographically weighted regression. Geographical Analysis 52, 87-106. Hurvich, C. M., Simonoff, J. S. and Tsai, C.-L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. JRSS B 60, 271-293. da Silva, A. R. and Fotheringham, A. S. (2016). The multiple testing issue in geographically weighted regression. Geographical Analysis 48, 233-247.