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#' @title Moran's Index at lag of 1
#'
#' @description This functions computes the Moran's spatial correlation index
#' (with lag one). It also computes a null value obtained by randomizing
#' the matrix.
#'
#' @references
#'
#' Dakos, V., van Nes, E. H., Donangelo, R., Fort, H., &
#' Scheffer, M. (2010). Spatial correlation as leading indicator of
#' catastrophic shifts. Theoretical Ecology, 3(3), 163-174.
#'
#' Legendre, P., & Legendre, L. F. J. (2012). Numerical Ecology.
#' Elsevier Science.
#'
#' @param input An matrix or a list of matrix object. It should
#' be a square matrix
#'
#' @param subsize logical. Dimension of the submatrix used to coarse-grain the
#' original matrix (set to 1 for no coarse-graining).
#'
#' @param nreplicates Number of replicates to produce to estimate null
#' distribution of index (default: 999).
#'
#' @return A list (or a list of those if input is a list of matrix
#' object) of:
#' \itemize{
#' \item `value`: Spatial autocorrelation of the matrix
#' }
#' If nreplicates is above 2, then the list has the following additional
#' components :
#' \itemize{
#' \item `null_mean`: Mean autocorrelation of the null distribution
#' \item `null_sd`: SD of autocorrelation in the null distribution
#' \item `z_score`: Z-score of the observed value in the null distribution
#' \item `pval`: p-value based on the rank of the observed autocorrelation
#' in the null distribution.
#' }
#'
#' @examples
#'
#' \dontrun{
#' data(serengeti)
#'
#' # One matrix
#' indicator_moran(serengeti[1])
#'
#' # Several matrices
#' indicator_moran(serengeti)
#' }
#'
#'@export
indicator_moran <- function(input,
subsize = 1, # default = no cg
nreplicates = 999) {
check_mat(input) # checks if binary and sensible
# We do not check for binary status as moran's I can be computed on both.
if (is.list(input)) {
# Returns a list of lists
return( lapply(input, indicator_moran, subsize, nreplicates) )
} else {
# We alter the moran function to do coarse_graining if the user asked for it
# (and not whether the matrix is binary or not).
if ( subsize > 1 ) {
indicf <- with_coarse_graining(raw_moran, subsize)
} else {
indicf <- raw_moran
}
return( compute_indicator_with_null(input, nreplicates, indicf) )
}
}
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