Compute Moran's I

A simple function to compute Moran's I, called by moran.test and moran.mc; $$I = \frac{n}{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}} \frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}(x_i-\bar{x})(x_j-\bar{x})}{\sum_{i=1}^{n}(x_i - \bar{x})^2} $$

Usage

moran(x, listw, n, S0, zero.policy=attr(listw, "zero.policy"), NAOK=FALSE)

Arguments

x: a numeric vector the same length as the neighbours list in listw
listw: a listw object created for example by nb2listw
n: number of zones
S0: global sum of weights
zero.policy: default attr(listw, "zero.policy") as set when listw was created, if attribute not set, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
NAOK: if 'TRUE' then any 'NA' or 'NaN' or 'Inf' values in x are passed on to the foreign function. If 'FALSE', the presence of 'NA' or 'NaN' or 'Inf' values is regarded as an error.

Value

a list of

I: Moran's I
K: sample kurtosis of x

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.

Author

Roger Bivand Roger.Bivand@nhh.no

Examples

data(oldcol)
col.W <- nb2listw(COL.nb, style="W")
crime <- COL.OLD$CRIME
str(moran(crime, col.W, length(COL.nb), Szero(col.W)))
#> List of 2
#>  $ I: num 0.511
#>  $ K: num 2.23
is.na(crime) <- sample(1:length(crime), 10)
str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE))
#> Warning: NAs in lagged values
#> List of 2
#>  $ I: num 0.142
#>  $ K: num 2.82