mc: The Moran coefficient (Moran's I)

In geostan: Bayesian Spatial Analysis

The Moran coefficient (Moran's I)

Description

The Moran coefficient, a measure of spatial autocorrelation (also known as Global Moran's I)

Usage

mc(x, w, digits = 3, warn = TRUE, na.rm = FALSE)

Arguments

x	Numeric vector of input values, length n.
w	An n x n spatial connectivity matrix. See shape2mat.
digits	Number of digits to round results to.
warn	If FALSE, no warning will be printed to inform you when observations with zero neighbors or NA values have been dropped.
na.rm	If na.rm = TRUE, observations with NA values will be dropped from both x and w.

Details

The formula for the Moran coefficient (MC) is

MC = \frac{n}{K}\frac{\sum_i \sum_j w_{ij} (y_i - \overline{y})(y_j - \overline{y})}{\sum_i (y_i - \overline{y})^2}

where n is the number of observations and K is the sum of all values in the spatial connectivity matrix W, i.e., the sum of all row-sums: K = \sum_i \sum_j w_{ij}.

If any observations with no neighbors are found (i.e. any(Matrix::rowSums(w) == 0)) they will be dropped automatically and a message will print stating how many were dropped. (The alternative would be for those observations to have a spatial lage of zero, but zero is not a neutral value.)

Value

The Moran coefficient, a numeric value.

Source

Chun, Yongwan, and Daniel A. Griffith. Spatial Statistics and Geostatistics: Theory and Applications for Geographic Information Science and Technology. Sage, 2013.

Cliff, Andrew David, and J. Keith Ord. Spatial processes: models & applications. Taylor & Francis, 1981.

See Also

moran_plot, lisa, aple, gr, lg

Examples

library(sf)
data(georgia)
w <- shape2mat(georgia, style = "W")
x <- georgia$ICE
mc(x, w)

geostan documentation built on April 3, 2025, 10:04 p.m.