MI.vec {spfilteR}

Local Moran Coefficient

Description

Reports the local Moran Coefficient for each unit.

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

Usage

MI.local(x, W, alternative = "greater")

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

Details

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

Value

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

Ii

observed value of local Moran's I

EIi

expected value of local Moran coefficients

VarIi

variance of local Moran's I

zIi

standardized local Moran coefficient

pIi

p-value of the test statistic

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

Note

The calculation of the statistic and its moments follows Anselin (1995) and Sokal et al. (1998).

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.

Author(s)

Sebastian Juhl

References

Anselin, Luc (1991): Local Indicators of Spatial Association-LISA. Geographical Analysis, 27 (2): pp. 93 - 115.

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

Sokal, Robert R., Neal L. Oden, Barbara A. Thomson (1998): Local Spatial Autocorrelation in a Biological Model. Geographical Analysis, 30 (4): pp. 331 - 354.

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.

See Also

MI.vec, MI.ev, MI.sf, MI.resid, MI.decomp

MI.resid, MI.local

Examples

data(fakedata)
x <- fakedataset$x2

(MIi <- MI.local(x = x, W = W, alternative = "greater"))

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

(MI <- MI.vec(x = X, W = W, alternative = "greater", symmetrize = TRUE))