R/mlink.test.R

In jfrench/smerc: Statistical Methods for Regional Counts

#' Maximum Linkage spatial scan test
#'
#' \code{mlink.test} implements the Maximum Linkage spatial
#' scan test of Costa et al. (2012). Starting with a single
#' region as a current zone, new candidate zones are
#' constructed by combining the current zone with the
#' connected region that maximizes the resulting likelihood
#' ratio test statistic, with the added constraint that the
#' region has the maximum connections (i.e., shares a border
#' with) with the regions in the current zone.  This
#' procedure is repeated until the population or distance
#' upper bounds constraints are reached.  The same procedure
#' is repeated for each region.  The clusters returned are
#' non-overlapping, ordered from most significant to least
#' significant. The first cluster is the most likely to be a
#' cluster. If no significant clusters are found, then the
#' most likely cluster is returned (along with a warning).
#'
#' The maximum intercentroid distance can be found by
#' executing the command:
#' \code{gedist(as.matrix(coords), longlat = longlat)},
#' based on the specified values of \code{coords} and
#' \code{longlat}.
#'
#' @inheritParams dmst.test
#' @return Returns a \code{smerc_cluster} object.
#' @author Joshua French
#' @export
#' @seealso \code{\link{print.smerc_cluster}},
#' \code{\link{summary.smerc_cluster}},
#' \code{\link{plot.smerc_cluster}},
#' \code{\link{scan.stat}}, \code{\link{scan.test}}
#' @references Costa, M.A. and Assuncao, R.M. and Kulldorff,
#'   M. (2012) Constrained spanning tree algorithms for
#'   irregularly-shaped spatial clustering, Computational
#'   Statistics & Data Analysis, 56(6), 1771-1783.
#'   <doi:10.1016/j.csda.2011.11.001>
#' @examples
#' data(nydf)
#' data(nyw)
#' coords <- with(nydf, cbind(longitude, latitude))
#' out <- mlink.test(
#'   coords = coords, cases = floor(nydf$cases),
#'   pop = nydf$pop, w = nyw,
#'   alpha = 0.12, longlat = TRUE,
#'   nsim = 2, ubpop = 0.05, ubd = 0.1
#' )
#' # better plotting
#' if (require("sf", quietly = TRUE)) {
#'    data(nysf)
#'    plot(st_geometry(nysf), col = color.clusters(out))
#' }
mlink.test <- function(coords, cases, pop, w,
                       ex = sum(cases) / sum(pop) * pop,
                       nsim = 499, alpha = 0.1, ubpop = 0.5,
                       ubd = 1, longlat = FALSE, cl = NULL) {
  # sanity checking
  arg_check_scan_test(coords, cases, pop, ex, nsim, alpha,
    nsim + 1, ubpop, longlat, FALSE,
    k = 1, w = w
  )

  coords <- as.matrix(coords) # ensure proper format
  N <- nrow(coords) # number of regions
  ty <- sum(cases) # sum of all cases

  # intercentroid distances
  d <- gedist(as.matrix(coords), longlat = TRUE)
  # upperbound for zone population
  max_pop <- ubpop * sum(pop)
  # find all neighbors from each starting zone within distance upperbound
  nn <- nndist(d, ubd)

  all_zones <- mst.all(nn,
    cases = cases, pop = pop, w = w,
    ex = ex, ty = ty, max_pop = max_pop,
    type = "all", nlinks = "max", early = FALSE,
    cl = cl, progress = FALSE
  )
  # extract relevant information
  nn2 <- lapply(all_zones, getElement, name = "locids")
  tobs <- unlist(lapply(all_zones, getElement, name = "loglikrat"),
    use.names = FALSE
  )
  # determine distinct zones
  wdup <- nndup(nn2, N)

  # remove zones with a test statistic of 0 or don't have
  # min number of cases or are duplicted
  w0 <- which(tobs == 0 | wdup)

  # determine zones
  zones <- nn2zones(nn2)

  # remove zones with a test statistic of 0
  zones <- zones[-w0]
  tobs <- tobs[-w0]

  # compute test statistics for simulated data
  if (nsim > 0) {
    message("computing statistics for simulated data:")
    tsim <- mlink.sim(
      nsim = nsim, nn = nn, ty = ty,
      ex = ex, w = w, pop = pop,
      max_pop = max_pop, cl = cl
    )
    pvalue <- mc.pvalue(tobs, tsim)
  } else {
    pvalue <- rep(1, length(tobs))
  }

  # significant, ordered, non-overlapping clusters and
  # information
  pruned <- sig_noc(
    tobs = tobs, zones = zones,
    pvalue = pvalue, alpha = alpha,
    order_by = "tobs"
  )

  smerc_cluster(
    tobs = pruned$tobs, zones = pruned$zones,
    pvalue = pruned$pvalue, coords = coords,
    cases = cases, pop = pop, ex = ex,
    longlat = longlat, method = "maximum linkage",
    rel_param = list(
      type = "poisson",
      simdist = "multinomial",
      nsim = nsim,
      ubpop = ubpop,
      ubd = ubd
    ),
    alpha = alpha,
    w = w, d = NULL
  )
}