Fit the Low-Level LHWR Model

Fit local weighted least-squares regressions from a prepared response vector, model matrix, distance matrix, and bandwidth vector. This function is the computational engine behind lhwr() and assumes that all model inputs have already been constructed.

Usage

hgwr.fit(y, X, D, bw, kernel = hgwr_kernel_names(), return_hat = TRUE)

Arguments

y

Numeric response vector of length n.

X

Numeric n x p model matrix. The first column should usually be an intercept if an intercept is desired.

D

Numeric n x n pairwise distance matrix used to construct kernel weights for each focal location.

bw

Positive bandwidth value or numeric vector of length n. A scalar is recycled to all focal locations; a vector supplies one radius per location.

kernel

Kernel used to convert distances into local weights. Available choices are "bisquare", "gaussian", "exponential", "tricube", and "boxcar".

return_hat

Logical. If TRUE, compute hat-matrix diagnostics and unscaled local standard-error components.

Value

A list with local coefficient matrix beta_hat, local standard errors se_beta, local t-values t_beta, fitted values y_hat, residuals, residual sum of squares RSS, hat-matrix traces trS and trStS, AICc, diagnostic summaries, effective bandwidth vector, hat-matrix diagonal, local condition numbers, local effective sample sizes, and local counts of positive kernel weights.

Examples

set.seed(2)
H <- simulate_H2(40, r_max = 2)
D <- hyperbolic_distance_matrix(H$Z)
X <- cbind(Intercept = 1, x = rnorm(40))
y <- 1 + 2 * X[, "x"] + rnorm(40, sd = 0.2)
bw <- rep(1.5, 40)

fit <- hgwr.fit(y, X, D, bw, kernel = "gaussian")
fit$AICc
head(fit$beta_hat)