moran_bv {spdep}

Compute the Global Bivariate Moran's I

Description

Given two continuous numeric variables, calculate the bivariate Moran's I. See details for more.

Usage

moran_bv(x, y, listw, nsim = 499, scale = TRUE)

Arguments

x

a numeric vector of same length as y.

y

a numeric vector of same length as x.

listw

a listw object for example as created by nb2listw().

nsim

the number of simulations to run.

scale

default TRUE.

Details

The Global Bivariate Moran is defined as

I_B = \frac{\Sigma_i(\Sigma_j{w_{ij}y_j\times x_i})}{\Sigma_i{x_i^2}}

It is important to note that this is a measure of autocorrelation of X with the spatial lag of Y. As such, the resultant measure may overestimate the amount of spatial autocorrelation which may be a product of the inherent correlation of X and Y. The output object is of class "boot", so that plots and confidence intervals are available using appropriate methods.

Value

An object of class "boot", with the observed statistic in component t0.

Author(s)

Josiah Parry [e-mail]

References

Wartenberg, D. (1985), Multivariate Spatial Correlation: A Method for Exploratory Geographical Analysis. Geographical Analysis, 17: 263-283. doi:10.1111/j.1538-4632.1985.tb00849.x

Examples

data(boston, package = "spData")
x <- boston.c$CRIM
y <- boston.c$NOX
listw <- nb2listw(boston.soi)
set.seed(1)
res_xy <- moran_bv(x, y, listw, nsim=499)
res_xy$t0
boot::boot.ci(res_xy, conf=c(0.99, 0.95, 0.9), type="basic")
plot(res_xy)
set.seed(1)
lee_xy <- lee.mc(x, y, listw, nsim=499, return_boot=TRUE)
lee_xy$t0
boot::boot.ci(lee_xy, conf=c(0.99, 0.95, 0.9), type="basic")
plot(lee_xy)
set.seed(1)
res_yx <- moran_bv(y, x, listw, nsim=499)
res_yx$t0
boot::boot.ci(res_yx, conf=c(0.99, 0.95, 0.9), type="basic")
plot(res_yx)
set.seed(1)
lee_yx <- lee.mc(y, x, listw, nsim=499, return_boot=TRUE)
lee_yx$t0
boot::boot.ci(lee_yx, conf=c(0.99, 0.95, 0.9), type="basic")
plot(lee_yx)