The Moran coefficient, a measure of spatial autocorrelation (also known as Global Moran's I)
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.
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.
Returns
The Moran coefficient, a numeric value.
Details
The formula for the Moran coefficient (MC) is
MC=Kn∑i(yi−y)2∑i∑jwij(yi−y)(yj−y)
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=∑i∑jwij.
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.)