# Area-based Rao’s index.

#### Matteo Marcantonio

#### 2025-09-02

    require(rasterdiv)
    require(terra)
    require(rasterVis)
    require(RColorBrewer)
    require(viridis)
    require(latticeExtra)
    require(ggplot2)

This vignette uses rasterdiv to derive classic and multidimension area-based Rao’s index from an input vector layer and multiple raster layers.

## Overview

A SpatRaster called copNDVI is loaded together with the package rasterdiv. copNDVI is a 8-bit raster, meaning that pixel values range from 0 to 255. You could stretch it to match a more familiar (-1,1) values range using `terra::stretch(copNDVI,minv=-1,maxv=1)`. The original dataset was resampled to 1/10th of its spatial resolution and pixels with values 253, 254 and 255 (water) were set as NA’s.

    copNDVI <- load_copNDVI()
    copNDVIlr <- terra::aggregate(copNDVI, fact=10)
    values(copNDVIlr) <- as.integer(values(copNDVIlr))
    world <- load_world()

## Compute Area based Rao’s Index

    RaoC <- paRao(x=copNDVIlr, area=world, field='CONTINENT', alpha=c(1,2))

    #Plot classic area-based Rao's index
    plot(RaoC, col=hcl(RaoC$alpha.1*10), main="Classic Rao's index per continent alpha 1")
    text(RaoC, label=paste("Rao'Q =", round(RaoC$alpha.1,1)), col="black", family="Arial", halo=TRUE)

## Compute multidimension area-based Rao’s Index

    # Adding a second "noise" SpatRaster layer
    # copNDVIlr <- terra::aggregate(copNDVI, fact=20)
    values(copNDVIlr) <- as.integer(values(copNDVIlr))
    noise = rast(copNDVIlr)
    noise[] = as.integer(runif(n=ncell(noise),min=1, max=10))
    RaoMC <- paRao(x=c(copNDVIlr,noise), area=world, field='CONTINENT', alpha=2, method="multidimension", simplify=0)

    #Plot area-based Rao's index
    plot(RaoMC, col=hcl(RaoMC$alpha.2*10000), main="Multidimension Rao's index per continent alpha 10")
    text(RaoMC, label=paste("Rao'Q =", round(RaoMC$alpha.2,3)), col="black", family="Arial", halo=TRUE)

## Additional example subsetting on a continent and then using a grid vector to derive Rao’s in each cell

    #Subset
    africa <- subset(world, world$CONTINENT=="Africa")

    #Make the raster grid
    africa.r <- rast(ext(africa), nrow=20, ncol=20, crs = "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0")
    africa.r[] <- 1:ncell(africa.r)

    #Vectorise the SpatRaster
    africa.v = as.polygons(africa.r)

    #Derive Rao's (alpha=2) for each grid cell
    RaoGRID <- paRao(x=copNDVIlr, area=africa.v, field='lyr.1', alpha=2, simplify=0, na.tolerance=0.2)

    #Transform the spatial polygon data frame in a raster layer that can be used in levelplot
    rr <- rast(RaoGRID, ncol=20, nrow=20)
    values(rr) <- RaoGRID$alpha.2

    #Plot Rao's per grid cell
    ggplot() +
      geom_raster(data = as.data.frame(rr, xy=TRUE), aes(x = x, y = y, fill = lyr.1)) +
      scale_fill_viridis(option = "D", direction = 1) +
       geom_polygon(data = fortify(as(africa.v, "Spatial")), aes(x = long, y = lat, group = group), fill = NA, color = "grey", linewidth=0.3) +
      geom_polygon(data = fortify(as(world, "Spatial")), aes(x = long, y = lat, group = group), fill = NA, color = "black", , linewidth=0.5) +
      theme(legend.position = "none", aspect.ratio = 0.5)