Fit geographically weighted lasso, ridge, or elastic net

The three wrappers use the same normalized local least-squares loss, neighbor structure and preprocessing convention. Ridge applies a quadratic penalty, lasso an absolute-value penalty, and elastic net a mixture controlled by alpha. Positive ridge uses a direct Cholesky solve; an unsuccessful solve is reported as a failed fit. Lasso and elastic net use coordinate updates. Coefficients are returned on the original predictor scale.

Usage

gwr_lasso_fit(
  x,
  y,
  coords = NULL,
  neighbors = NULL,
  k = NULL,
  kernel = c("bisquare", "gaussian", "exponential", "tricube", "boxcar"),
  bandwidth = NULL,
  lambda,
  standardize = TRUE,
  control = gwrs_control()
)

gwr_ridge_fit(
  x,
  y,
  coords = NULL,
  neighbors = NULL,
  k = NULL,
  kernel = c("bisquare", "gaussian", "exponential", "tricube", "boxcar"),
  bandwidth = NULL,
  lambda,
  standardize = TRUE,
  control = gwrs_control()
)

gwr_en_fit(
  x,
  y,
  coords = NULL,
  neighbors = NULL,
  k = NULL,
  kernel = c("bisquare", "gaussian", "exponential", "tricube", "boxcar"),
  bandwidth = NULL,
  lambda,
  alpha = 0.5,
  standardize = TRUE,
  control = gwrs_control()
)

Arguments

x

Numeric design matrix without an intercept.

y

Numeric response vector.

coords

Optional coordinate matrix used to construct neighbors.

neighbors

Optional reusable object from [gwr_neighbors()].

k

Number of neighbors when `neighbors` is not supplied.

kernel

Spatial kernel.

bandwidth

Fixed distance bandwidth. The default `NULL` uses the farthest retained neighbor as an adaptive bandwidth at each target.

lambda

Nonnegative regularization strength.

standardize

Whether predictors are standardized globally before the local fits. Coefficients are returned on the original scale.

control

Numerical controls from [gwrs_control()].

alpha

Mixing parameter in `[0, 1]`.

Value

An object of class `gwr_sl_fit` and `gwrs_fit`.

Examples

quake <- datasets::quakes[1:30, ]
coords <- as.matrix(quake[, c("long", "lat")])
x <- as.matrix(quake[, c("depth", "stations")])
neighbors <- gwr_neighbors(coords, k = 18)
control <- gwrs_control(n_threads = 1)

lasso <- gwr_lasso_fit(
  x, quake$mag, neighbors = neighbors, lambda = 0.05, control = control
)
ridge <- gwr_ridge_fit(
  x, quake$mag, neighbors = neighbors, lambda = 0.05, control = control
)
elastic_net <- gwr_en_fit(
  x, quake$mag, neighbors = neighbors, lambda = 0.05,
  alpha = 0.6, control = control
)
c(lasso = lasso$alpha, ridge = ridge$alpha, elastic_net = elastic_net$alpha)