acorrelogram_mc

##  4) acorrelogram_mc()  ##

# DESCRIPTION: calculates Moran's I (acoef = "I") or Geary's c (acoef = "c") for each bin in 'nblist'
# Significance of autocorrelation coefficient is tested via spdep::mantel.mc or spdep::geary.mc

# RETURNS: S3 class object of type 'spclist'/'list'
# 'spclist' can be passed to plot.spclist() to plot the correlogram

# REQUIRES: a data vector (x) and corresponding "nblist" from binneR()

# ARGUMENTS:
#
# acoef : the autocorrelation coefficient to be calculated (default = "I")
# 
#    "I": Moran's I
#    "c": Geary's c
#
# nsim : the number of randomizations (default = 9999)
# ...  : other arguments to be passed to moran.mc() or geary.mc()


# START
acorrelogram_mc <- function(x, nblist, acoef = "I", nsim = 9999, ...){

  if (class(nblist)[1] != "nblist"){
    stop("This function requires an object of class 'nblist'; use binneR() to create an 'nblist' object.")
  }	

  if (length(x) != length(nblist$bin_list[[1]]$neighbours)){
    stop("Length of vector x is not equal to the number of samples used to create the object of class 'nb'.")
  }

  if (class(nblist)[1] == "mlist"){
    stop("You have provided an object of type 'mlist' rather than an object of type 'nblist'.")
  }

  auto_vect <- numeric(length(nblist$bin_list))
  Pval <- numeric(length(auto_vect))

  if (acoef == "I"){
	
    measure <- "Moran's I"
    auto_exp <- - (length(x) - 1) ^ -1
    
    for (i in 1:length(nblist$bin_list)){
      I_mc <- spdep::moran.mc(x, nblist$bin_list[[i]], nsim = nsim, zero.policy = TRUE, ...)
      auto_vect[i] <- I_mc$statistic		
        if (I_mc$statistic >= auto_exp){
          your_p <- sum(I_mc$res >= I_mc$statistic) / length(I_mc$res)
        } else if(I_mc$statistic < auto_exp){
          your_p <- sum(I_mc$res <= I_mc$statistic) / length(I_mc$res)
        }
      Pval[i] <- your_p
    }

  } else if (acoef == "c"){
    
    measure <- "Geary's c"
    auto_exp <- 1

    for (i in 1:length(nblist$bin_list)){
      c.mc <- spdep::geary.mc(x, nblist$bin_list[[i]], nsim = nsim, zero.policy = TRUE,...)
      auto_vect[i] <- c.mc$statistic
        if (c.mc$statistic >= auto_exp){
          your_p <- sum(c.mc$res >= c.mc$statistic) / length(c.mc$res)
        } else if(c.mc$statistic < auto_exp){
          your_p <- sum(c.mc$res <= c.mc$statistic) / length(c.mc$res)
        }
      Pval[i] <- your_p
    }
  }
				
  autolist <-list(coefficient = measure, 
                  null_expected = auto_exp, 
                  estimates = auto_vect, 
                  P_vals = Pval, 
                  type = nblist$type, 
                  boundaries = nblist$boundaries)
  
  class(autolist) <- c("spclist", class(autolist))

return(autolist)
}		
# END

# names(autolist)
# measure : the autocorrelation coefficient that was calculated
#           "Moran's I" or "Geary's c"
# null_expected : the expected value of Moran's I or Geary's c (for length(x))
# estimates : vector of estimated autocorrelation coefficients
# P_vals : vector of P-values
# type : the type of bins
# boundaries : upper limits of each bin