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Lorentz-Hyperbolic Moran's I Diagnostic for LHWR Residuals

Source: R/moran.R
moran.lhwr.Rd

Compute the Lorentz-hyperbolic Moran's I diagnostic (LH-Moran's I) for hyperbolic residual autocorrelation from a fitted LHWR model. By default, the neighborhood weights define hyperbolic neighborhoods from Lorentz-hyperbolic distances stored in the fitted object.

Usage

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
)

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

An object of class "hgwr_moran" containing Moran's I, expected I, permutation p-value, and settings.

Details

These are descriptive fitted-residual diagnostics, not exact post-fit tests: smoothing makes residuals nonexchangeable. The global permutation expectation is -1/(n-1) for a fixed nonconstant vector and fixed zero-diagonal weights, not the sampling expectation of estimated LHWR residuals. Two-sided p-values use absolute deviations from that expectation and a plus-one correction. A count of B permutations gives p-value increments of 1/(B+1).

Supply nondefault diagnostic geometry, kernel and bandwidth settings explicitly. They are not all inherited from the fitted model. The direct kernel choices are bisquare, Gaussian and exponential; use an explicit W for other kernels. A supplied W determines the diagnostic, so default labels in the returned object do not describe how that matrix was constructed. Validate its dimensions, row order, finite nonnegative entries and isolated rows. Its diagonal is zeroed, then optional row standardization is applied.

Stored kNN lists are reused only for compact bisquare diagnostic weights. Gaussian and exponential diagnostics use the full distance matrix, retaining their nonzero tails beyond the adaptive k-neighbour radius. This requires quadratic memory in the number of observations. An explicit W remains supported for user-defined diagnostic weights. See vignette("lhwr-diagnostics-and-tuning", package = "LHWL") for formulas, reproducible examples and explicit weight construction.

Examples

set.seed(12)
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)
moran.lhwr(fit, permutations = 99)