Global Moran's I (spatial autocorrelation)

Do neighbouring countries have similar values? Global Moran's I on the country spine, with a permutation pseudo-p-value. No spdep required: at ~200 countries the dense arithmetic is trivial.

Usage

morans_i(data, value, scale = "small", n_perm = 999, weights = NULL)

Arguments

data: A country-level data frame with iso3c (map-ready frames are reduced to one row per country first).
value: The value column (unquoted).
scale: Natural Earth resolution for the default contiguity adjacency (see country_borders()). Ignored when weights is supplied.
n_perm: Number of permutations for the pseudo-p-value (default 999; use 0 to skip the test, which leaves p_value as NA).
weights: A country_weights() object. Defaults to land-border contiguity, row-standardised – which excludes every island. See below.

Value

A one-row tibble: i (observed Moran's I), expected (\(-1/(n-1)\) under no autocorrelation), n (countries used), n_excluded (countries with data that the weights could not reach), n_links, p_value (one-sided, \(P(I_{perm} \ge I_{obs})\), computed as \((1 + \#\{I^{*} \ge I_{obs}\}) / (n_{perm} + 1)\), so never exactly zero – the floor is \(1/(n_{perm}+1)\)) and an excluded list-column of the excluded iso3c codes. Set a seed beforehand for a reproducible p_value.

Which countries are left out

The default weights are land-border contiguity, and an island has no land border – so any country with no land neighbour present in data drops out entirely. On the bundled world_snapshot that is around a quarter of the countries with data: Japan, the United Kingdom, Australia, Indonesia, Madagascar, New Zealand, the Philippines, Iceland, Cuba, Sri Lanka and every small island state. The omission is systematic rather than random.

n_excluded and excluded report it, and country_weights() fixes it – "knn" and "distance" give every country neighbours:

morans_i(snap, gdp_per_capita, weights = country_weights("knn", k = 5))

References

Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika 37(1/2), 17-23. doi:10.2307/2332142

Examples

# \donttest{
snap <- countryatlas::world_snapshot$countries
set.seed(42)
# every country included, no sf required
morans_i(snap, gdp_per_capita, n_perm = 99,
         weights = country_weights("knn", k = 5))
#> # A tibble: 1 × 7
#>       i expected     n n_excluded n_links p_value excluded 
#>   <dbl>    <dbl> <int>      <int>   <int>   <dbl> <list>   
#> 1 0.472 -0.00532   189          2     785    0.01 <chr [2]>
# }