Local Moran's I (LISA)

Local Indicators of Spatial Association (Anselin 1995): one Moran statistic per country, plus the cluster type it belongs to. Where morans_i() answers "is there clustering anywhere", this answers "where, and of what kind".

Usage

local_morans(data, value, weights = NULL, n_perm = 999, alpha = 0.05)

Arguments

data

A country-level frame with iso3c and the value column.

value

The value column (unquoted).

weights

A country_weights() object. Defaults to land-border contiguity, which excludes islands – prefer country_weights("knn") for global work.

n_perm

Permutations for the pseudo-p-value (default 999; use 0 to skip the test, which leaves p_value as NA).

alpha

Significance threshold for the cluster label (default 0.05).

Value

A tibble, one row per country: iso3c, value, lag (the neighbour average), ii (the local statistic), p_value and cluster ("High-High", "Low-Low", "High-Low", "Low-High" or "Not significant").

p_value is a two-sided pseudo-p from conditional permutation: \((1 + \#\{|I_i^{*}| \ge |I_i|\}) / (n_{perm} + 1)\), so it is never exactly zero and its floor is \(1/(n_{perm}+1)\) – with the default 999 permutations, 0.001. Two-sided because a local statistic is interesting at both ends: a country surrounded by unlike neighbours is as much a finding as one surrounded by like ones. cluster is "Not significant" wherever p_value > alpha, and everywhere when n_perm = 0 leaves it NA. Set a seed beforehand for a reproducible p_value.

References

Anselin, L. (1995). Local Indicators of Spatial Association – LISA. Geographical Analysis 27(2), 93-115. doi:10.1111/j.1538-4632.1995.tb00338.x

See also

lisa_map(), morans_i(), country_weights()

Examples

# \donttest{
snap <- countryatlas::world_snapshot$countries
set.seed(1)
local_morans(snap, gdp_per_capita, weights = country_weights("knn", k = 5),
             n_perm = 99)
#> # A tibble: 189 × 6
#>    iso3c  value     lag      ii p_value cluster        
#>    <chr>  <dbl>   <dbl>   <dbl>   <dbl> <fct>          
#>  1 ABW   33374.  14921. -0.0529    0.86 Not significant
#>  2 AGO    2845.   2910.  0.286     0.13 Not significant
#>  3 ALB    6549.  10395.  0.102     0.54 Not significant
#>  4 AND   41035. 101542.  2.73      0.01 High-High      
#>  5 ARE   41605.  30830.  0.448     0.18 Not significant
#>  6 ARG   12774.  10806.  0.0407    0.53 Not significant
#>  7 ARM    5378.   8064.  0.152     0.41 Not significant
#>  8 ATG   18350.  28266.  0.0151    0.64 Not significant
#>  9 AUS   61481.   1840. -0.935     0.14 Not significant
#> 10 AUT   45959.  38625.  0.833     0.05 High-High      
#> # ℹ 179 more rows
# }