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## neg_exp_profile
## Jamie Spaulding
#' Negative Exponential Model for Geographic Profiling
#' @description An implementation of variations of the negative exponential
#' decay model for serial crime analysis. In this model, the decline is at
#' a constant rate, therefore the likelihood of the perpetrator's home base
#' drops quickly from the incident locations until it approaches zero
#' likelihood. The user can select different variants including the 'CrimeStat'
#' base model, the 'Dragnet' model, or whether a buffer and plateau is present
#' at the start of the decay function. This model assumes that the likelihood
#' of the serial perpetrator's home base decreases in a exponential fashion
#' as the distance increases from the crime incidents.
#' @param lat a vector of latitudes for the crime incident series
#' @param lon a vector of latitudes for the crime incident series
#' @param method 'CrimeStat', 'Dragnet', or a custom parameter based negative exponential
#' decay function. If using the 'CrimeStat' or 'Dragnet' method, values do not
#' need to be provided from 'a' and 'b' as the default parameters will be
#' used. Default parameters for the 'CrimeStat' are: \eqn{a = 1.89} \eqn{a = -0.06}.
#' Default parameters for the 'Dragnet' are: \eqn{a = b = 1}. If using a custom
#' model, values must be provided for '*a*' and '*b*'.
#' @param buffer TRUE/FALSE. Whether a buffer zone where a likelihood of zero
#' is fit around the incidents and a plateau of peak likelihood is fit prior
#' to the negative exponential decay. The function calculates the buffer zone
#' and the plateau area to each be half of the average nearest neighbor
#' distance.
#' @param a the slope coefficient which defines the function decrease in distance
#' @param b exponential multiplier for the distance decay function
#' @return A data frame of points depicting a spatial grid of the hunting area
#' for the given incident locations. Also given are the resultant summed
#' values (score) for each map point. A higher resultant score indicates
#' a greater the probability that point contains the offender's anchor point.
#' @param n total number of cells within the spatial grid for the jeopardy surface.
#' If \code{NULL}, the default value for '*n*' is 40,000.
#' @author Jamie Spaulding, Keith Morris
#' @references Ned Levine, \emph{CrimeStat IV: A Spatial Statistics Program for the
#' Analysis of Crime Incident Locations (version 4.0)}. Ned Levine & Associates,
#' Houston, TX, and the National Institute of Justice, Washington, DC, June 2013.
#' @references D Canter, T Coffey, M Huntley & C Missen. (2000). \emph{Predicting
#' serial killers' home base using a decision support system.} Journal of
#' quantitative criminology, 16(4), 457-478.
#' @keywords spatial methods
#' @examples
#' \dontshow{
#' data(desalvo)
#' test <- neg_exp_profile(desalvo$lat, desalvo$lon, method = "CrimeStat", n = 4)
#' }
#' \donttest{
#' #Using provided dataset for the Boston Strangler Incidents:
#' data(desalvo)
#' test <- neg_exp_profile(desalvo$lat, desalvo$lon, method = "CrimeStat")
#' g_map = sp::SpatialPixelsDataFrame(points = test[c("lons", "lats")], data = test)
#' g_map <- raster::raster(g_map)
#' # Assign a Coordinate Reference System for the Raster
#' raster::crs(g_map) <- sp::CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")
#' # Define a Parula Color Pallete for Resultant Jeopardy Surface
#' library(leaflet) #for mapping the geographic profile
#' pal <- colorNumeric(pals::parula(200), raster::values(g_map),
#' na.color = "transparent")
#' leaflet() %>%
#' addTiles() %>%
#' addProviderTiles('Esri.WorldTopoMap', group = 'Topo') %>%
#' addAwesomeMarkers(lng = -71.07357, lat = 42.41322, icon =
#' awesomeIcons(icon = 'home', markerColor = 'green'), popup = 'Residence') %>%
#' addRasterImage(g_map, colors = pal, opacity = 0.6) %>%
#' addLegend(pal = pal, values = raster::values(g_map), title = 'Score') %>%
#' addCircleMarkers(lng = desalvo$lon, lat = desalvo$lat, radius = 4, opacity = 1,
#' fill = 'black', stroke = TRUE, fillOpacity = 0.75, weight = 2,
#' fillColor = "red")
#' }
#' @importFrom geosphere distHaversine
#' @importFrom RANN nn2
#' @importFrom utils txtProgressBar
#' @importFrom utils setTxtProgressBar
#' @export
neg_exp_profile <- function(lat, lon, method = c("CrimeStat", "Dragnet", "Custom"),
buffer = FALSE, a = NULL, b = NULL, n = NULL){
# Set Defaults -----
if (method == "Custom" & is.null(a)) {
stop("If using a custom model, both 'a' and 'b' must be specified")
}
if (method == "Custom" & is.null(b)) {
stop("If using a custom model, both 'a' and 'b' must be specified")
}
if (method == "CrimeStat") {
a <- 1.89
b <- -0.06
}# Levine (2013)
if (method == "Dragnet") {
a <- 1
b <- -1
} #Canter et al. (2000)
if (is.null(n)) {n <- 40000}
# Computation of Map Boundaries/ Hunting Area -----
lat_max <- max(lat) + ((max(lat) - min(lat)) / (2 * (length(lat) - 1)))
lat_min <- min(lat) - ((max(lat) - min(lat)) / (2 * (length(lat) - 1)))
lon_max <- max(lon) + ((max(lon) - min(lon)) / (2 * (length(lon) - 1)))
lon_min <- min(lon) - ((max(lon) - min(lon)) / (2 * (length(lon) - 1)))
# Calculate Range of Bounding Box -----
lat_range <- lat_max - lat_min
lon_range <- lon_max - lon_min
# Determine Sequence of Lat and Lon Gridlines -----
g_size <- sqrt(n)
lats <- seq(lat_min,lat_max, length.out = g_size)
lons <- seq(lon_min,lon_max, length.out = g_size)
# Create a Run Sequence for Each Incident of Grid Points -----
run_seq <- expand.grid(lats, lons)
names(run_seq) <- c("lats", "lons")
if (buffer == TRUE) {
# Calculate Incident Buffer Zone -----
dat_nn <- cbind(lat,lon) # Extract only lat and lon columns
nn_list <- RANN::nn2(dat_nn, dat_nn, k=2) # Find NNs
nn <- nn_list$nn.idx # Extract NN pairs
# Calculate Distances Between NN Pairs -----
nn_d <- NULL
jj <- 1
for(i in 1:nrow(nn)){
incid1 <- dat_nn[nn[i,1],]
incid2 <- dat_nn[nn[i,2],]
nn_d[jj] <- geosphere::distHaversine(p1 = c(incid1[2], incid1[1]),
p2 = c(incid2[2], incid2[1]),
r = 3958) # hold y (lat) constant
jj <- jj+1
}
plat_zone <- mean(nn_d) #Canter et al. (2000)
buf_zone <- (mean(nn_d)) / 2 #Canter et al. (2000)
jj <- 1
output <- data.frame()
# Progress Bar
pb = utils::txtProgressBar(min = 0, max = length(lat) * n, style = 3)
tick <- 0
for(i in 1:length(lat)){
for(j in 1:nrow(run_seq)){
tick <- tick + 1
utils::setTxtProgressBar(pb, tick)
xn <- lon[i]
yn <- lat[i]
xi <- run_seq$lons[j]
yi <- run_seq$lats[j]
d <- geosphere::distHaversine(p1 = c(xn, yn),
p2 = c(xi, yi),
r = 3958)
if(d < buf_zone) {out <- 0}
if(d >= buf_zone & d < plat_zone) {out <- 1}
if(d > plat_zone) {out <- (a * exp(b * (d - buf_zone)))}
output[jj,i] <- out
jj <- jj+1
}
jj <- 1
}
} else{
jj <- 1
output <- data.frame()
pb = txtProgressBar(min = 0, max = length(lat) * n, style = 3)
tick <- 0
for(i in 1:length(lat)){
for(j in 1:nrow(run_seq)){
tick <- tick + 1
utils::setTxtProgressBar(pb, tick)
xn <- lon[i]
yn <- lat[i]
xi <- run_seq$lons[j]
yi <- run_seq$lats[j]
d <- geosphere::distHaversine(p1 = c(xn, yn),
p2 = c(xi, yi),
r = 3958)
output[jj,i] <- a * exp(b * d)
jj <- jj+1
}
jj <- 1
}
}
# Summation of Values for Each Grid Point -----
sums <- rowSums(output, na.rm = TRUE)
dat <- cbind(sums, run_seq)
return(dat)
}
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