moran_bv function

Compute the Global Bivariate Moran's I

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

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.

Returns

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

Details

The Global Bivariate Moran is defined as

c("$\n$", "$I_B = \\frac{\\Sigma_i(\\Sigma_j{w_{ij}y_j\\times x_i})}{\\Sigma_i{x_i^2}}\n$")

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.

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)

References

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

Author(s)

Josiah Parry josiah.parry@gmail.com