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Spatial Analysis

Spatial Analysis. Grid cell counts. Grid Methods. Data are recorded as coming from a particular area, but we do not have exact coordinates Screened artifacts from an excavation unit, census data (population counts from survey tracts, incidence of disease or other characteristic.

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Spatial Analysis

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  1. Spatial Analysis Grid cell counts

  2. Grid Methods • Data are recorded as coming from a particular area, but we do not have exact coordinates • Screened artifacts from an excavation unit, census data (population counts from survey tracts, incidence of disease or other characteristic

  3. Spatial Clusters • Null hypothesis is that the data are distributed according to a Poisson distribution • Variance/mean ratio (VMR) provides a rough indication of clustering where VMR = 1 is a Poisson distribution, <1 is regular and >1 clustered

  4. Visualizing Counts • Choropleth maps represent quantity or category by shading polygons • Dot density maps represent quantity/density by randomly or regularly spaced symbols within the polygon

  5. Package sp • Definitions for spatial objects • SpatialPolygons are an object that contains a set of places (e.g. grid cells, states, counties) each of which can include multiple polygons and/or holes • Perfect for choropleth and dot density maps

  6. # Create a Spatial Polygons object source("GridUnits3a.R") # Append first line of coordinates to the bottom so # first-coord= last-coord Quads <- lapply(Quads, function(x) rbind(x, x[1,])) # Load package sp for spatial classes library(sp) # Create Polygon list (one from each unit) QuadsList<- lapply(Quads, function(x) Polygon(x, hole=FALSE)) # Areas3a <- sapply(QuadsList, function(x) x@area) to get areas # Create a Polygons list Units <- lapply(1:20, function(x) Polygons(QuadsList[x], UnitLbl[x])) # Create a Spatial Polygons list SPUnits <- SpatialPolygons(Units, 1:20) # sapply(1:20, function(x) SPUnits@polygons[[x]]@area) # to get areas from SpatialPolygons

  7. opar <- par(mfrow=c(2, 2), mar=c(0, 0, 0, 0)) plot(SPUnits, col=gray(1:20/20)) plot(SPUnits, col=rainbow(20)) plot(SPUnits, col=rainbow(20, start=0, end=4/6)) plot(SPUnits, density=c(6:25), angle=c(45, -45)) plot(SPUnits, density=c(6:25), angle=c(-45, 45), add=TRUE) par(opar)

  8. # Load FlkSize3a FlkDen3a <- round(sweep(FlkSize3a[,c("TCt", "TWgt")], 1, FlkSize3a$Area, "/"), 1) FlkDen3a <- data.frame(East=FlkSize3a$East, North=FlkSize3a$North, FlkDen3a) var(FlkDen3a$TCt)/mean(FlkDen3a$TCt) # Cut into 4 groups TCtGrp1 <- cut(FlkDen3a$TCt, quantile(FlkDen3a$TCt, c(0:4/4)), include.lowest=TRUE, dig=4) # TCtGrp2 <- cut(FlkDen3a$TCt, quantile(FlkDen3a$TCt, c(0:4/4)), # labels=1:4, include.lowest=TRUE) # TCtGrp3 <- cut(FlkDen3a$TCt, 0:4*1250+25, include.lowest=TRUE, # dig=4) Colors <- rev(rainbow(4, start=0, end=4/6)) Gray <- rev(gray(1:4/4)) Hatch <- c(5, 10, 15, 20)

  9. opar <- par(mfrow=c(2, 2), mar=c(0, 0, 0, 0)) plot(SPUnits, col=Colors[as.numeric(TCtGrp1)]) text(985, 1015.75, "Total Flakes", cex=1.25) legend(985.5, 1022, levels(TCtGrp1), fill=Colors) plot(SPUnits, col=Gray[as.numeric(TCtGrp1)]) text(985, 1015.75, "Total Flakes", cex=1.25) legend(985.5, 1022, levels(TCtGrp1), fill=Gray) plot(SPUnits, angle=45, density=Hatch[as.numeric(TCtGrp1)]) plot(SPUnits, angle=-45, density=Hatch[as.numeric(TCtGrp1)], add=TRUE) text(985, 1015.75, "Total Flakes", cex=1.25) legend(985.5, 1022, levels(TCtGrp1), angle=45, density=Hatch) legend(985.5, 1022, levels(TCtGrp1), angle=-45, density=Hatch) par(opar)

  10. library(maptools) opar <- par(mfrow=c(2, 2), mar=c(0, 0, 0, 0)) for (i in 1:4) { dots <- dotsInPolys(SPUnits, as.integer(round(FlkDen3a$TCt/50, 0))) # 1 dot = 50 flakes plot(SPUnits, lty=0) points(dots, pch=20, col="red") polygon(c(982,982,983,983,984.5,985,985,987,987,986.2,985,985, 984.5,984,983.5,983,982.7,982.5),c(1015.5,1021,1021,1022, 1022,1021.3,1018,1018,1017.6,1017,1017,1016.9,1016.8,1016.6, 1016.3, 1016,1015.6,1015.5), lwd=2, border="black") } par(opar) dots <- dotsInPolys(SPUnits, as.integer(round(FlkDen3a$TCt/50, 0)), f="regular") plot(SPUnits, lty=0) points(dots, pch=20, cex=.75, col="red") polygon(c(982,982,983,983,984.5,985,985,987,987,986.2,985,985,984.5, 984,983.5,983,982.7,982.5),c(1015.5,1021,1021,1022,1022,1021.3, 1018,1018,1017.6,1017,1017,1016.9,1016.8,1016.6,1016.3, 1016,1015.6,1015.5), lwd=2, border="black") text(985, 1015.75, "Total Flakes \n(Each dot = 50 flakes)", cex=1.25)

  11. Countour Mapping • We fit a model to the data to interpolate between the observations and smooth them • Trend surface models with polynomials • Kriging – developed in geophysics to interpolate and extrapolate

  12. library(geoR) # load FlkDen3a.RData FlkDen3a$East <- FlkDen3a$East + .5 FlkDen3a$North <- FlkDen3a$North + .5 FlkDen3a$AvWgt <- FlkDen3a$TWgt/FlkDen3a$TCt columns <- names(FlkDen3a) Flakes3a <- as.geodata(FlkDen3a, 1:2, 3:5, c("TCt", "TWgt", "AvWgt")) GridPts <- expand.grid(East=seq(982, 987, .25), North=seq(1015.5, 1022, .25)) Border3a <- cbind(c(982,982,983,983,984.5,985,985,987,987,986.2, 985,985,984.5,984,983.5,983,982.7,982.5),c(1015.5,1021,1021, 1022,1022,1021.3,1018,1018,1017.6,1017,1017,1016.9,1016.8, 1016.6,1016.3,1016,1015.6,1015.5)) V <- variog(Flakes3a, data=Flakes3a$data[,"TCt"]) plot(V, type="b") vf <- variofit(V) TCtKv <- krige.conv(Flakes3a, data=Flakes3a$data[,"TCt"], locations=GridPts, krige=krige.control(cov.pars=c(1292000, .824))) contour(TCtKv, borders=Border3a, xlab="East", ylab="North") contour(TCtKv, borders=Border3a, axes=FALSE) contour(TCtKv, borders=Border3a, filled=TRUE) persp(TCtKv, borders=Border3a, xlab="East", ylab="North", zlab="Total Flakes", expand=.5)

  13. Unconstrained Clustering • Proposed by Robert Whallon • Take grid data and computer percentages (areas defined by relative abundance, not density) • Cluster grids and plot the distribution of the clusters to identify activity areas

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