moranbir.test {bispdep}

Moran's Ixy test using Monte Carlo permutations for bivariate spatial autocorrelation

Description

Moran's Ixy test for bivariate spatial autocorrelation using a spatial weights matrix in weights list form. Constructs a plot of the empirical density from the simulations (Monte Carlo permutations) and superimposes Moran's bivariate Ixy index.

Usage

moranbir.test(varX,varY,listw,zero.policy=NULL,adjust.n=TRUE,N,graph=FALSE,
              alternative="greater", spChk=NULL, print.results=TRUE, ...)

Arguments

varX

a numeric vector of the same length as the neighbours list in listw with the values of the variable x

varY

a numeric vector of the same length as the neighbours list in listw with the values of the variable y

listw

a listw object created for example by nb2listw

zero.policy

by default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE stop with error for any empty neighbours sets and assign NA.

adjust.n

default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted

N

set the number of spatial permutations for the calculation.

graph

by default = FALSE. Use TRUE to create test's graphic.

alternative

a character string specifying the alternative hypothesis, must be one of greater (default), less or two.sided.

spChk

should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()

print.results

by default = TRUE. Use FALSE to hide test results (table). Results are: observed, expected and p-value.

...

other parameters similar to original

Details

Compare the observed bivariate Moran's Ixy (moran.bi function) with the expected value empirical density. The expected value is -cor(x,y)/(n-1), where n is the number of rows/samples (number of polygons), and represents the null hyphothesis (Ho) of no spatial Autocorrelation (bivariate Moran's Ixy coefficient around zero). This expected value density is constructed with Monte Carlo simulations. Values significant below of -cor(x,y)/(n-1) represents negative spatial autocorrelation (generally negative values of observed bivariate Moran's Ixy), and values significant above of -cor(x,y)/(n-1) represents positive spatial autocorrelation (generally positive values of observed bivariate Moran's Ixy). For hypothesis testing the sample values are compared with empirical density, and p-value is calculated. For significant values of p-value (reject Ho), the conclusion of the test could be: "given the value of p-value, there is less than alpha (1%, or 5%, or 10%) likelihood that the pattern (clustered or dispersed) could be the result of random change".

Value

A list with class htest containing the following components:

Observed

the value of the observed Moran's Ixy.

Expected

the expected value of Moran's Ixy.

p.value

the p-value of the test.

Values

corresponds to the N simulated values of Moran's Ixy coefficient for bivariate autocorrelation.

Links

Adapted from:

1. Spatial Autocorrelation (Moran’s I) Test

2. Moran's I Test

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 21; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi:10.1007/s11749-018-0599-x

See Also

moran.bi, moranbi.mc, listw2U

Examples

library(spdep)
data(columbus)
data(oldcol)
columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE)
plot(st_geometry(columbus))
col_nbq <- poly2nb(columbus)
a.lw <- nb2listw(col_nbq, style="W")
set.seed(123)
RCrimeInc.Q <- moranbir.test(columbus$CRIME,columbus$INC,a.lw,graph=TRUE,
                             zero.policy =TRUE,N=1000)
RCrimeInc.Q$Values


COL.k4.nb <- knn2nb(knearneigh(coords, 4))
RCrimeInc.Knn <- moranbir.test(columbus$CRIME, columbus$INC, listw2U(nb2listw(COL.k4.nb,
                               style="W")),graph=TRUE,zero.policy =TRUE,N=1000)
RCrimeInc.Knn