Lorentz-Hyperbolic LISA Diagnostic (LH-LISA) for LHWR Residuals

Compute the Lorentz-hyperbolic LISA diagnostic (LH-LISA), that is local Moran's I under hyperbolic neighborhoods, for residuals from a fitted LHWR model. The default weights use Lorentz-hyperbolic distance to define each hyperbolic neighborhood.

Usage

local_moran.lhwr(
  object,
  W = NULL,
  distance = c("lorentz", "euclidean"),
  kernel = c("bisquare", "gaussian", "exponential"),
  bandwidth = NULL,
  adaptive = TRUE,
  k = NULL,
  permutations = 999,
  row_standardize = TRUE,
  seed = NULL
)

local_moran.hgwr(
  object,
  W = NULL,
  distance = c("lorentz", "euclidean"),
  kernel = c("bisquare", "gaussian", "exponential"),
  bandwidth = NULL,
  adaptive = TRUE,
  k = NULL,
  permutations = 999,
  row_standardize = TRUE,
  seed = NULL
)

Arguments

object

An object returned by lhwr().

W

Optional numeric n x n neighborhood weight matrix. If supplied, it is used directly after diagonal entries are set to zero.

distance

Distance used when W = NULL. "lorentz" uses intrinsic Lorentz-hyperbolic distance on the Lorentz hyperboloid and is the default. "euclidean" is an explicit fallback using ordinary Euclidean distance on the projected (z1, z2) coordinates.

kernel

Kernel used to convert distances into weights.

bandwidth

Optional fixed bandwidth. If omitted and adaptive = TRUE, the fitted model bandwidth or k is used as the adaptive neighbor count.

adaptive

Logical. If TRUE, use adaptive nearest-neighbor radii.

k

Optional adaptive neighbor count. Overrides bandwidth for adaptive weights.

permutations

Number of random permutations for the p-value. Use zero to skip permutation inference.

row_standardize

Logical. If TRUE, row-standardize weights.

seed

Optional random seed used for permutation inference.

Value

A data frame of class "hgwr_local_moran" with local Moran values, permutation p-values, z-scores, and Lorentz-hyperbolic LISA cluster labels.

Details

The local statistic is the centred residual times its weighted residual lag, divided by the mean squared centred residual. High/low classifications refer to these two centred quantities, not response levels or coefficient signs. The full residual vector is permuted, rather than keeping the focal residual fixed. Two-sided absolute deviations use each location's permutation mean; p-values use a plus-one correction. These are descriptive post-fit checks, not exact tests for fitted residuals.

cluster_type uses raw p-values <= 0.05 and does not apply multiplicity adjustment. Changing the plot's alpha only masks stored classifications when requested; it does not reclassify or adjust p-values. Keep raw classifications and any explicitly adjusted display in separate columns. Adjustment alone does not validate the fitted-residual permutation law. Record permutations and seed separately, as not all settings are stored in the local result.

The diagnostic weight and kernel-specific cache rules described in moran.lhwr() apply here too. See vignette("lhwr-diagnostics-and-tuning", package = "LHWL") and vignette("lhwr-graphics", package = "LHWL") for tables, cluster maps, Moran scatterplots and explicit adjusted display rules.

Examples

set.seed(13)
H <- simulate_H2(60, r_max = 3)
x <- rnorm(60)
y <- 1 + 2 * x + rnorm(60, sd = 0.3)
fit <- lhwr(y ~ x, data.frame(y, x), Z = H$Z, bw = 25)
lm <- local_moran.lhwr(fit, permutations = 99)
head(lm)
plot(lm)