Spatial correlogram over neighbour-graph lag orders

For each lag \(k = 1, \dots, order\) the units at shortest-path distance exactly \(k\) in the neighbour graph (spdep::nblag) are coded with style and a global statistic is computed, as spdep::sp.correlogram: Moran's I with expectation \(-1/(n-1)\) and its randomisation or normality variance (spdep::moran.test), Geary's C with expectation 1 (spdep::geary.test), or the Pearson correlation of x with its lag-k spatial lag. \(n\) in the moments counts units with a lag-k neighbour. The deviate is (estimate - expectation) / sqrt(variance) with a two-sided normal p-value.

Usage

SpatialCorrelogram(
  adjacency,
  x,
  order = 1L,
  method = "I",
  style = "W",
  randomisation = TRUE
)

Arguments

adjacency: Neighbour indicator matrix (nonzero = neighbour).
x: Numeric vector.
order: Largest lag order.
method: "I", "C" or "corr".
style: Weight coding "W", "B", "C" or "U".
randomisation: Randomisation (else normality) variance.

Value

List with estimate, expectation, variance, z, p_value (by lag; only estimate for "corr"), n_with_neighbours, method, style.

References

Cliff, A. D. and Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion, London.

Examples

A <- 1 * (abs(outer(1:8, 1:8, "-")) == 1)
SpatialCorrelogram(A, c(1, 2, 3, 5, 4, 6, 8, 7), order = 2)$estimate
#> [1] 0.797619 0.250000