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,
  p_adjust = c("fdr", "bonferroni", "holm", "none")
)

Arguments

data

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

value

The value column (unquoted).

weights

A country_weights() object. NULL (default) uses country_weights("knn", k = 5): every country's five nearest neighbours, islands included. country_weights("contiguity") gives the land-border default of earlier versions, which leaves every island out.

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.

p_adjust

For local = TRUE, how to adjust the per-country p-values for multiple testing: "fdr" (default), "bonferroni", "holm" or "none", as in local_morans(). The global form makes one test and takes no adjustment.

Value

With local = TRUE, a tibble of iso3c, gi_star, z_score, p_value (two-sided, from the normal approximation) and p_adjusted, 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: 199 × 5
#>    iso3c gi_star z_score  p_value p_adjusted
#>    <chr>   <dbl>   <dbl>    <dbl>      <dbl>
#>  1 ABW   0.0139    0.449 0.654        0.850 
#>  2 AFG   0.00109  -1.07  0.287        0.794 
#>  3 AGO   0.00162  -1.00  0.316        0.794 
#>  4 ALB   0.00476  -0.629 0.529        0.831 
#>  5 AND   0.0408    3.58  0.000337     0.0134
#>  6 ARE   0.0207    1.26  0.207        0.794 
#>  7 ARG   0.00672  -0.388 0.698        0.850 
#>  8 ARM   0.00381  -0.727 0.467        0.802 
#>  9 ATG   0.0133    0.340 0.734        0.850 
#> 10 AUS   0.0180    0.898 0.369        0.794 
#> # ℹ 189 more rows
# }