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

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

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.

- 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`

.

The Moran coefficient, a numeric value.

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 is for those observations to have a spatial lage of zero---but zero is not a neutral value, see the Moran scatter plot.

moran_plot, lisa, aple, gr, lg