nonormmoran: Detection of spatial autocorrelation
In GeoXp: Interactive exploratory spatial data analysis

Description Usage Arguments Details Value Note Author(s) References See Also Examples

The function nonnormmoran is used to detect spatial autocorrelation in the residuals u from the least squares model Y=beta X+u. It calculates Moran's I statistic of the residuals based on the gaussian asymptotic distribution and give a p-value associated to the test of spatial autocorrelation (gaussian version).

1	nonormmoran(y, x, W)

`y`	vector of size n of dependent variable
`x`	matrix n x p containing explanatory variables
`W`	spatial weight matrix

W is supposed standartized :

I=(n/s)frac(u'Wu)(u'u)

I sim N(E(I),var(I))

let M=(I-X(X'X)^(-1)X')

E(I)=(n/s)frac(tr(MW))(n-k)

d=frac(n-p)(n+p+2)

V(I)=(n/s)^2[tr(MWMW')+tr(MW)^2+(tr(MW))^2]/d-E(I)^2

Z_I=frac(I-E(I))(v(I)^(1/2))

When W is row-normalised, s=n else s is the number of nonzero links

a list with nobs is the number of observations, nvar, the number of explanatory variables, morani is the Moran's I statistic estimate, imean is E(I), ivar is var(I), istat is the normalized Moran's I statistic (corresponding to Z_i), and prob the associated p-value.

This function is closed to the function lm.morantest included in the spdep package. nonnormmoran is less confortable to use because it didn't take into account S4 classes.

Translated into R from Jim Lessage's Spatial Econometrics Toolbox, http://www.spatial-econometrics.com/

Thibault Laurent, Anne Ruiz-Gazen, Christine Thomas-Agnan (2012), GeoXp: An R Package for Exploratory Spatial Data Analysis. Journal of Statistical Software, 47(2), 1-23.

moranplotmap,neighbourmap,makeneighborsw,normw

###
# data baltimore
data(baltimore)

# a spatial weight matrix constructed in the matrix format
W <- makeneighborsw(cbind(baltimore$X,baltimore$Y),method="neighbor",4)

# when W is not row-normalised ...
nonormmoran(baltimore$PRICE,cbind(rep(1,nrow(baltimore)),baltimore[,14:15]),W)
# when W is row_normalised ...
nonormmoran(baltimore$PRICE,cbind(rep(1,nrow(baltimore)),baltimore[,14:15]),normw(W))

# If we compare to the function lm.morantest
baltimore.lm<-lm(PRICE~LOTSZ+SQFT,data=baltimore)

lm.morantest(baltimore.lm, mat2listw(W))