spfilteR (version 2.1.0)

MI.decomp: Decomposition of the Moran Coefficient

Description

A decomposition of the Moran coefficient in order to separately test for the simultaneous presence of positive and negative autocorrelation in a variable.

Usage

MI.decomp(x, W, nsim = 100, na.rm = TRUE)

Value

Returns a data.frame that contains the following information for each variable:

I+

observed value of Moran's I (positive part)

VarI+

variance of Moran's I (positive part)

pI+

simulated p-value of Moran's I (positive part)

I-

observed value of Moran's I (negative part)

VarI-

variance of Moran's I (negative part)

pI-

simulated p-value of Moran's I (negative part)

pItwo.sided

simulated p-value of the two-sided test

Arguments

x

a vector or matrix

W

spatial connectivity matrix

nsim

number of iterations to simulate the null distribution

na.rm

listwise deletion of observations with missing values (TRUE/ FALSE)

Author

Sebastian Juhl

Details

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

The p-values calculated for I+ and I- assume a directed alternative hypothesis. Statistical significance is assessed using a permutation procedure to generate a simulated null distribution.

References

Dary, Stéphane (2011): A New Perspective about Moran’s Coefficient: Spatial Autocorrelation as a Linear Regression Problem. Geographical Analysis, 43 (2): pp. 127 - 141.

See Also

MI.vec, MI.ev, MI.sf, MI.resid, MI.local, getEVs

Examples

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

(MI.dec <- MI.decomp(x = X, W = W, nsim = 100))

# the sum of I+ and I- equals the observed Moran coefficient:
I <- MI.vec(x = X, W = W)[, "I"]
cbind(MI.dec[, "I+"] + MI.dec[, "I-"], I)