Moran's I for spatial autocorrelation of diversity

Computes Moran's I for a numeric site attribute (for example a Hill number or a model residual) using inverse-distance weights among sites. A permutation p-value is returned. Implemented natively so callers do not need spdep; when spdep is installed, tests compare the two.

Usage

geo_moran(
  data,
  value,
  lon = lon,
  lat = lat,
  site = NULL,
  nperm = 999,
  correlogram = FALSE,
  bins = 5,
  seed = NULL
)

Arguments

data: A data frame of sites with coordinates and a value column, or an sf table (its point coordinates are used).
value: <data-masking> Numeric column to test.
lon, lat: Coordinate columns (ignored for sf input). Longitude and latitude give great-circle distances in metres; projected coordinates (values outside the longitude/latitude range, or a projected sf table) give straight-line distances in the CRS units.
site: Optional site column for labels in the correlogram.
nperm: Number of permutations for the p-value.
correlogram: If TRUE, also return a simple distance-bin correlogram.
bins: Number of distance bins for the correlogram.
seed: Optional RNG seed for permutations.

Value

A tibble (tmr_geo_moran) with Moran's I, the expected value under randomness, the variance under normality, a two-sided permutation p-value, and optional correlogram rows in attribute correlogram.

References

Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37, 17-23. doi:10.2307/2332142

Examples

set.seed(1)
# Positive spatial autocorrelation along a gradient
g <- expand.grid(x = 1:6, y = 1:6)
g$val <- g$x + 0.3 * rnorm(nrow(g))
geo_moran(g, val, lon = x, lat = y, nperm = 199)
#> # A tibble: 1 × 7
#>   statistic expectation variance p.value     n nperm method                     
#>       <dbl>       <dbl>    <dbl>   <dbl> <int> <dbl> <chr>                      
#> 1     0.267     -0.0286 0.000530   0.005    36   199 Moran's I (inverse-distanc…