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Calculate Moran's I

Source: R/calc_MoransI.R
calc_MoransI.Rd

Calculate Moran's I

Usage

calc_MoransI(
  object,
  df_neighbours = NULL,
  spatial_autocorrelation = TRUE,
  compute_pseudo_p = FALSE,
  tested_moransI = NULL,
  n_permutations = 999,
  ignore_borders = FALSE,
  return_intermediate_values = FALSE
)

Arguments

object

RLum.Results or numeric (required) containing the values of the grains of one. Should have length 100; can contain NA values.

df_neighbours

data.frame (with default): a data frame with 3 columns (location, neighbour and weight, respectively), with each row indicating the index of one location and one of its neighbours (note that the concept of "location" versus "neighbour" is symmetric, so each neighbouring pair needs to be specified only once), alongside their relative weight (generally set to 1). If NULL (default), this is constructed automatically by the internal function .get_Neighbours.

spatial_autocorrelation

logical (with default): whether spatial autocorrelation should be considered in the computation of Moran's I (TRUE by default). If FALSE, the function computes Moran's I expected value in case of no autocorrelation (H_0). See details for further information.

compute_pseudo_p

logical (with default): whether a pseudo p-value should be computed (FALSE by default).

tested_moransI

numeric (with default): The value of Moran's I to be tested against when computing the pseudo p-value. If NULL (default), the value calculated by the function will be used. Ignored if compute_pseudo_p is FALSE.

n_permutations

integer (with default): number of random permutations tested to calculate the fraction which is the pseudo p (defaults to 999). Influences the calculation speed, which will have impact in case of large scale simulation loops. Ignored if compute_pseudo_p is FALSE.

ignore_borders

logical (with default): whether only grain locations that do not lie on the border of the disc should be considered (FALSE by default). Thus if TRUE, only the inner 8x8 grain locations rather than the full 10x10 are considered. Ignored if df_neighbours is not NULL or if spatial_autocorrelation = FALSE.

return_intermediate_values

logical (with default): whether the function should return a list with several intermediate calculation results (defaults to FALSE). Ignored if spatial_autocorrelation is FALSE.

Value

By default one numerical value, roughly between -1 and 1, where close to zero means no spatial correlation, and value close to 1 a positive spatial correlation given the pattern we interested in (by default all rook neighbours). A value closer to -1 has no meaning within the context of luminescence crosstalk. If compute_pseudo_p = TRUE, then the computed pseudo p-value is returned. If return_intermediate_values is set to TRUE, a list with several values used for calculation is returned instead of a single outcome.

Details

Case of no spatial autocorrelation

Perhaps a bit counter-intuitive, the expected value of Moran's I under the null hypothesis of no spatial correlation is a value slightly smaller than zero. When setting spatial_autocorrelation = FALSE, this function calculates the expected value based on the number of observations or the length of the observation vector (while taking out NA values). Note that the expected value only depends on the number of observed separate grain values. This can be useful for plotting.

The expected Moran's I for the null hypothesis of no spatial correlation corresponds to -1 / (n - 1), with n being the number of non-missing observations.

How to cite

Boer, A.d., Steinbuch, L., 2025. calc_MoransI(): Calculate Moran's I. In: Kreutzer, S., Burow, C., Dietze, M., Fuchs, M.C., Schmidt, C., Fischer, M., Friedrich, J., Mercier, N., Philippe, A., Riedesel, S., Autzen, M., Mittelstrass, D., Gray, H.J., Galharret, J., Colombo, M., Steinbuch, L., Boer, A.d., 2025. Luminescence: Comprehensive Luminescence Dating Data Analysis. R package version 1.0.0. https://r-lum.github.io/Luminescence/

References

de Boer, A-M., Steinbuch, L., Heuvelink, G.B.M., Wallinga, J., 2025. A novel tool to assess crosstalk in single-grain luminescence detection. Submitted.

Author

Anna-Maartje de Boer, Luc Steinbuch, Wageningen University & Research, 2025 , RLum Developer Team

Examples


## Test a fictional sample with spatial correlation
calc_MoransI(object = c(1:100))
#> [1] 0.8888889

## Test some fictional samples without spatial correlation;
## note the randomness with each repetition
calc_MoransI(object = rnorm(n = 100))
#> [1] -0.06706568
calc_MoransI(object = rnorm(n = 100))
#> [1] 0.01886048
calc_MoransI(object = rnorm(n = 100))
#> [1] 0.06968043