# Tidy and geospatial kernel density estimates with boundary and truncated kernels Tidy and geospatial versions of kernel density estimates with boundary and truncated kernels for 1- and 2-dimensional data. ```r tidy_kde_boundary(data, ...) tidy_kde_truncate(data, boundary, ...) st_kde_boundary(x, ...) st_kde_truncate(x, boundary, ...) ``` ## Arguments - `data`: data frame/tibble of data values - `x`: sf object with point geometry - `boundary`: data frame/sf point geometry of boundary - `...`: other parameters in `ks::kde.boundary` function ## Returns The outputs from `*_kde_boundary`, `*_kde_truncate` have the same structure as the standard kernel density estimate from `*_kde`. ## Details A boundary kernel density estimate is a modification of the standard density estimate for bounded data. There are two main types: beta kernels (`boundary.kernel="beta"`) and linear kernels (`boundary.kernel="linear"`). For details of the computation of the boundary kernel estimates and of the bandwidth selector procedure, see `ks::kde.boundary`. Currently only rectangular boundaries are supported, as defined by `xmin` x `xmax`. A truncated kernel density estimate is a modification of the standard density estimate for bounded data. All the probability mass outside of `boundary` is set to zero and re-assigned over the regions inside in the boundary. The boundary can be any polygon. For further details of the computation of the truncated kernel estimate, see `ks::kde.truncate`. For details of the computation of the boundary kernel estimates and the truncated kernel density estimates, and of the bandwidth selector procedure, see `ks::kde.boundary`, `ks::kde.truncate`. ## Examples ```r ## tidy boundary density estimates library(ggplot2) data(worldbank, package="ks") worldbank <- dplyr::as_tibble(worldbank) ## percentage data is bounded on [0,100] x [0,100] wb2 <- na.omit(worldbank[,c("internet", "ag.value")]) xmin <- c(0,0); xmax <- c(100,100) rectb <- data.frame(x=c(0,100,100,0,0), y=c(0,0,100,100,0)) ## standard density estimate t1 <- tidy_kde(wb2) ## tidy truncated density estimate t2 <- tidy_kde_truncate(wb2, boundary=rectb) tt <- rbind(t1, t2, labels=c("Standard KDE", "Truncated KDE")) tb <- contour_breaks(tt, group=FALSE) ## standard estimate exceeds boundary but not truncated estimate gr <- geom_polygon(data=rectb, aes(x=x,y=y), inherit.aes=FALSE, fill=NA, colour=1, linetype="dashed") gt <- ggplot(tt, aes(x=internet, y=ag.value)) gt + geom_contour_filled_ks(colour=1, breaks=tb) + gr + facet_wrap(~group) ## linear boundary density estimate ## beta boundary density estimate t3 <- tidy_kde_boundary(wb2, boundary.kernel="beta", xmin=xmin, xmax=xmax) t4 <- tidy_kde_boundary(wb2, boundary.kernel="linear", xmin=xmin, xmax=xmax) t5 <- rbind(t1, t2, t3, t4, labels=c("Standard KDE", "Truncated KDE", "Beta bd KDE", "Linear bd KDE")) tb <- contour_breaks(t5, group=FALSE) ## standard estimate exceeds boundary but not boundary or truncated estimates gt + geom_contour_filled_ks(data=t5, colour=1, breaks=tb) + gr + facet_wrap(~group) ## geospatial boundary density estimates data(wa) data(grevilleasf) hakeoides <- dplyr::filter(grevilleasf, species=="hakeoides") hakeoides_bbox <- sf::st_bbox(c(xmin=4e5, xmax=5.7e5, ymin=6.47e6, ymax=7e6), crs=sf::st_crs(hakeoides)) xminb <- hakeoides_bbox[1:2]; xmaxb <- hakeoides_bbox[3:4] hakeoides_bbox <- sf::st_as_sfc(hakeoides_bbox) hakeoides_crop <- sf::st_filter(hakeoides, hakeoides_bbox) s1 <- st_kde(hakeoides_crop) s2 <- st_kde_boundary(hakeoides_crop, boundary.kernel="beta", xmin=xminb, xmax=xmaxb) s3 <- st_kde_boundary(hakeoides_crop, boundary.kernel="linear", xmin=xminb, xmax=xmaxb) ## geospatial truncated density estimate s4 <- st_kde_truncate(x=hakeoides_crop, boundary=hakeoides_bbox) s5 <- rbind(s1, s2, s3, s4, labels=c("Standard KDE", "Beta bd KDE", "Linear bd KDE", "Truncated KDE")) ## base R plots xlim <- c(1.2e5, 1.1e6); ylim <- c(6.1e6, 7.2e6) cols <- colorspace::qualitative_hcl(n=4, palette="Set2") layout(matrix(c(1,3,2,4), ncol=2)) plot(wa, xlim=xlim, ylim=ylim) plot(hakeoides_bbox, add=TRUE, lty=3, lwd=2) plot(s1, add=TRUE, border=cols[1], col=NA, legend=FALSE) plot(wa, xlim=xlim, ylim=ylim) plot(hakeoides_bbox, add=TRUE, lty=3, lwd=2) plot(s2, add=TRUE, border=cols[2], col=NA, legend=FALSE) plot(wa, xlim=xlim, ylim=ylim) plot(hakeoides_bbox, add=TRUE, lty=3, lwd=2) plot(s3, add=TRUE, border=cols[3], col=NA, legend=FALSE) mapsf::mf_legend(type="symb", val=c("Standard KDE","Beta bd KDE", "Linear bd KDE", "Truncated KDE"), pal=cols, cex=rep(3,4), pch=rep("-",4), title="Density", pos="bottomleft") plot(wa, xlim=xlim, ylim=ylim) plot(hakeoides_bbox, add=TRUE, lty=3, lwd=2) plot(s4, add=TRUE, border=cols[4], col=NA, legend=FALSE) layout(1) ## geom_sf plots gs <- ggplot() + geom_sf(data=wa, fill=NA) + geom_sf(data=hakeoides_bbox, linetype="dotted", fill=NA) + ggthemes::theme_map() + colorspace::scale_colour_discrete_qualitative(palette="Set2") gs + geom_sf(data=st_get_contour(s5), aes(colour=group), fill=NA) + coord_sf(xlim=xlim, ylim=ylim) + guides(colour=guide_legend(title="Density")) + facet_wrap(~group) ```

tidyst_kde_boundary function