Local spatial statistics: hotspots and LISA clusters

Per-site statistics that say where values cluster, adding columns to data:

geo_hotspot(): the Getis-Ord \(G_i^*\) statistic (Getis and Ord 1992; Ord and Getis 1995) as a z-score, its two-sided p-value and a class ("hot", "cold" or "not significant"). The site itself is in its own neighbourhood, with binary weights.
geo_lisa(): local Moran's \(I_i\) (Anselin 1995) with row- standardised weights, its expectation, variance, z-score and p-value under conditional randomisation (Sokal, Oden and Thomson 1998), and the cluster type ("High-High", "Low-Low", "High-Low", "Low-High" or "not significant"). With nperm > 0 the p-value comes from conditional permutation instead.

Neighbours are the k nearest sites (default) or all sites within dist metres (great-circle). Values equal spdep::localG() and spdep::localmoran() for the same neighbours.

Many sites are tested at once, so consider adjusting p_value (for example p.adjust(p_value, "fdr")) before reading individual sites.

Usage

geo_hotspot(
  data,
  value,
  lon = lon,
  lat = lat,
  k = 5,
  dist = NULL,
  alpha = 0.05
)

geo_lisa(
  data,
  value,
  lon = lon,
  lat = lat,
  k = 5,
  dist = NULL,
  alpha = 0.05,
  nperm = 0,
  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.
k: Number of nearest neighbours (used when dist is NULL).
dist: Distance band in metres; overrides k.
alpha: Significance level for the class columns.
nperm: geo_lisa() only: number of conditional permutations for the p-value; 0 (default) uses the analytical randomisation variance.
seed: Optional RNG seed for permutations.

Value

data with columns gi_star, p_value and hotspot (geo_hotspot()), or lisa, lisa_expected, lisa_variance, lisa_z, p_value and cluster (geo_lisa()). Rows with a missing value or coordinate get NA. The neighbour definition is in attribute "neighbours".

References

Anselin, L. (1995). Local indicators of spatial association – LISA. Geographical Analysis, 27, 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x

Getis, A. and Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24, 189-206. doi:10.1111/j.1538-4632.1992.tb00261.x

Sokal, R. R., Oden, N. L. and Thomson, B. A. (1998). Local spatial autocorrelation in a biological model. Geographical Analysis, 30, 331-354. doi:10.1111/j.1538-4632.1998.tb00406.x

Ord, J. K. and Getis, A. (1995). Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27, 286-306. doi:10.1111/j.1538-4632.1995.tb00912.x

Examples

# The 16 real Mt Wilhelm ant transects (Mottl, Moses and Klimes 2023)
geo_hotspot(png_ants_sites, elevation, k = 3)
#> # A tibble: 16 × 10
#>    site   transect elevation_band elevation   lon   lat baits gi_star p_value
#>    <chr>     <int>          <int>     <int> <dbl> <dbl> <int>   <dbl>   <dbl>
#>  1 MW0200        1            200       216  145. -5.74    60 -2.49   0.0127 
#>  2 MW0200        2            200       249  145. -5.74    60 -2.49   0.0127 
#>  3 MW0700        1            700       716  145. -5.73    60 -2.01   0.0441 
#>  4 MW0700        2            700       774  145. -5.73    60 -2.01   0.0441 
#>  5 MW1200        1           1200      1166  145. -5.72    60 -2.01   0.0441 
#>  6 MW1200        2           1200      1089  145. -5.72    60 -2.01   0.0441 
#>  7 MW1700        1           1700      1638  145. -5.76    60 -1.44   0.150  
#>  8 MW1700        2           1700      1840  145. -5.76    60 -1.44   0.150  
#>  9 MW2200        1           2200      2398  145. -5.76    60  0.535  0.592  
#> 10 MW2200        2           2200      2339  145. -5.76    60  0.0774 0.938  
#> 11 MW2700        1           2700      2752  145. -5.81    60  0.962  0.336  
#> 12 MW2700        2           2700      2617  145. -5.81    60  0.962  0.336  
#> 13 MW3200        1           3200      3404  145. -5.80    60  2.97   0.00296
#> 14 MW3200        2           3200      3259  145. -5.81    60  2.97   0.00296
#> 15 MW3700        1           3700      3825  145. -5.79    60  2.97   0.00296
#> 16 MW3700        2           3700      3916  145. -5.78    60  2.97   0.00296
#> # ℹ 1 more variable: hotspot <fct>
geo_lisa(png_ants_sites, elevation, k = 3)
#> # A tibble: 16 × 13
#>    site   transect elevation_band elevation   lon   lat baits    lisa
#>    <chr>     <int>          <int>     <int> <dbl> <dbl> <int>   <dbl>
#>  1 MW0200        1            200       216  145. -5.74    60  1.48  
#>  2 MW0200        2            200       249  145. -5.74    60  1.47  
#>  3 MW0700        1            700       716  145. -5.73    60  0.910 
#>  4 MW0700        2            700       774  145. -5.73    60  0.886 
#>  5 MW1200        1           1200      1166  145. -5.72    60  0.683 
#>  6 MW1200        2           1200      1089  145. -5.72    60  0.728 
#>  7 MW1700        1           1700      1638  145. -5.76    60  0.236 
#>  8 MW1700        2           1700      1840  145. -5.76    60  0.117 
#>  9 MW2200        1           2200      2398  145. -5.76    60  0.0683
#> 10 MW2200        2           2200      2339  145. -5.76    60 -0.0123
#> 11 MW2700        1           2700      2752  145. -5.81    60  0.227 
#> 12 MW2700        2           2700      2617  145. -5.81    60  0.205 
#> 13 MW3200        1           3200      3404  145. -5.80    60  1.61  
#> 14 MW3200        2           3200      3259  145. -5.81    60  1.49  
#> 15 MW3700        1           3700      3825  145. -5.79    60  1.92  
#> 16 MW3700        2           3700      3916  145. -5.78    60  1.98  
#> # ℹ 5 more variables: lisa_expected <dbl>, lisa_variance <dbl>, lisa_z <dbl>,
#> #   p_value <dbl>, cluster <fct>