Moran Test for Spatial Autocorrelation

Tests for the presence of spatial autocorrelation in variables as indicated by the Moran coefficient. The variance is calculated under the normality assumption.

MI.vec(x, W, alternative = "greater", symmetrize = TRUE, na.rm = TRUE)

Arguments

x: a vector or matrix
W: spatial connectivity matrix
alternative: specification of alternative hypothesis as 'greater' (default), 'lower', or 'two.sided'
symmetrize: symmetrizes the connectivity matrix W by: 1/2 * (W + W') (TRUE/ FALSE)
na.rm: listwise deletion of observations with missing values (TRUE/ FALSE)

Value

Returns an object of class data.frame that contains the following information for each variable:

I: observed value of the Moran coefficient
EI: expected value of Moran's I
VarI: variance of Moran's I (under normality)
zI: standardized Moran coefficient
pI: p-value of the test statistic

Details

If x is a matrix, this function computes the Moran test for spatial autocorrelation for each column.

Note

Estimation of the variance (under the normality assumption) follows Cliff and Ord (1981), see also Upton and Fingleton (1985). It assumes the connectivity matrix W to be symmetric. For inherently non-symmetric matrices, it is recommended to specify symmetrize = TRUE.

References

Cliff, Andrew D. and John K. Ord (1981): Spatial Processes: Models & Applications. Pion, London.

Upton, Graham J. G. and Bernard Fingleton (1985): Spatial Data Analysis by Example, Volume 1. New York, Wiley.

Bivand, Roger S. and David W. S. Wong (2018): Comparing Implementations of Global and Local Indicators of Spatial Association. TEST 27: pp. 716 - 748.

Author

Sebastian Juhl

Examples

data(fakedata)
X <- cbind(fakedataset$x1, fakedataset$x2, fakedataset$x3)

(MI <- MI.vec(x = X, W = W, alternative = "greater", symmetrize = TRUE))
#>             I          EI        VarI        zI           pI    
#> 1 0.311178214 -0.01010101 0.005344193 4.3948248 5.543107e-06 ***
#> 2 0.168757531 -0.01010101 0.005344193 2.4466317 7.209904e-03  **
#> 3 0.009112739 -0.01010101 0.005344193 0.2628276 3.963417e-01