Getis-Ord G statistics (hot spots)

Global \(G\) and local \(G_i^*\): unlike Moran's I, these distinguish clusters of high values from clusters of low ones, which is what "hot spot" analysis usually wants.

Usage

getis_ord(data, value, weights = NULL, local = TRUE)

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.

local

If TRUE (default) return the per-country \(G_i^*\) with z-scores; if FALSE return the single global \(G\).

The global \(G\) needs a variable with a natural origin and no negative values: it compares cross-products, so negating the variable leaves it unchanged. Given a negative value it warns and returns NA rather than a number computed outside its domain. \(G_i^*\) standardises and is defined for signed data.

Value

With local = TRUE, a tibble of iso3c, gi_star, z_score and p_value (two-sided, from the normal approximation), one row per country used. With local = FALSE, a one-row tibble of g, expected, n (countries used – the same count, so the local form returns n rows) and n_links (non-zero weights).

References

Getis, A. & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis 24(3), 189-206. doi:10.1111/j.1538-4632.1992.tb00261.x

See also

local_morans(), country_weights()

Examples

# \donttest{
snap <- countryatlas::world_snapshot$countries
getis_ord(snap, gdp_per_capita, weights = country_weights("knn", k = 5))
#> # A tibble: 189 × 4
#>    iso3c gi_star z_score  p_value
#>    <chr>   <dbl>   <dbl>    <dbl>
#>  1 ABW   0.0147    0.453 0.650   
#>  2 AGO   0.00176  -0.982 0.326   
#>  3 ALB   0.00517  -0.602 0.547   
#>  4 AND   0.0435    3.59  0.000332
#>  5 ARE   0.0221    1.28  0.200   
#>  6 ARG   0.00720  -0.369 0.712   
#>  7 ARM   0.00410  -0.706 0.480   
#>  8 ATG   0.0142    0.362 0.717   
#>  9 AUS   0.0193    0.922 0.356   
#> 10 AUT   0.0258    1.66  0.0969  
#> # ℹ 179 more rows
# }