A local indicator of spatial association (LISA) based on Moran's I (the Moran coefficient) for exploratory data analysis.

`lisa(x, w, type = TRUE, scale = TRUE, digits = 3)`

Anselin, Luc. "Local indicators of spatial association—LISA." Geographical Analysis 27, no. 2 (1995): 93-115.

- x
Numeric vector of length

`n`

.- w
An

`n x n`

spatial connectivity matrix. See shape2mat. If`w`

is not row standardized (`all(Matrix::rowSums(w) == 1)`

), it will automatically be row-standardized.- type
Return the type of association also (High-High, Low-Low, High-Low, and Low-High)? Defaults to

`FALSE`

.- scale
If

`TRUE`

, then`x`

will automatically be standardized using`scale(x, center = TRUE, scale = TRUE)`

. If`FALSE`

, then the variate will be centered but not scaled, using`scale(x, center = TRUE, scale = FALSE)`

.- digits
Number of digits to round results to.

If `type = FALSE`

a numeric vector of lisa values for exploratory analysis of local spatial autocorrelation. If `type = TRUE`

, a `data.frame`

with columns `Li`

(the lisa value) and `type`

.

The values of `x`

will automatically be centered first with `z = scale(x, center = TRUE, scale = scale)`

(with user control over the `scale`

argument). The LISA values are the product of each `z`

value with the weighted sum of their respective surrounding value: $$I_i = z_i \sum_j w_{ij} z_j$$ (or in R code: `lisa = z * (w %*% z)`

). These are for exploratory analysis and model diagnostics.

An above-average value (i.e. positive z-value) with positive mean spatial lag indicates local positive spatial autocorrelation and is designated type "High-High"; a low value surrounded by high values indicates negative spatial autocorrelation and is designated type "Low-High", and so on.

This function uses Equation 7 from Anselin (1995). Note that the `spdep`

package uses Formula 12, which divides the same value by a constant term \(\sum_i z_i^2/n\). So the `geostan`

version can be made equal to the `spdep`

version by dividing by that value.

`moran_plot`

, `mc`

, `aple`

, `lg`

, `gr`