lmorn

Local Moran (LISA)

R

lmorn(x, w, nsim = 0, seed = NULL)

Anselin’s (1995) local indicator of spatial association for each unit: with z = x - mean(x) and m2 = mean(z^2), I_i = z_i / m2 sum_j w_ij z_j, its expectation and variance under total randomisation, the two-sided normal p-value, and a conditional permutation p-value: unit i keeps its value and its neighbours’ values are drawn without replacement from the others, nsim times from seed. The quadrant tells high-high and low-low clusters from high-low and low-high outliers. The p-values are per unit and not adjusted for the many tests made (use stats::p.adjust()); with row-standardised weights the sum of the I_i is S0 times global Moran’s I. That identity is proved in Lean: see proof("lmorn").

Parameters

x

The values: finite numbers, one per unit.

w

The weights: spwt()’s list, or an spdep listw object, for as many units as x.

nsim

The number of permutations: a whole number from 0.

seed

NULL to draw the simulations’ seed from R’s generator (so set.seed() fixes them), or one whole number from 0.

Returns

A data frame with one row per unit: ii (I_i), e, v, z, p, pperm ((1 + min(#{I* >= I}, #{I* <= I})) / (nsim + 1), NaN without permutations) and quad (1 high-high, 2 low-low, 3 low-high, 4 high-low, 0 neither).

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

Examples

set.seed(1)
p <- cbind(x = runif(60), y = runif(60))
v <- ifelse(p[, 1] > 0.7 & p[, 2] > 0.7, 5, 1) + rnorm(60, sd = 0.3)
l <- lmorn(v, spwt(p, k = 5), nsim = 199, seed = 1)
head(l)

Generated from the R help page: lmorn in the R reference.