# Spatial Autocorrelation

Tags :: Spatial Statistics

Simplest definition is that it represents relationship between nearby spatial units where each unit is encoded with a a realization of a single variable

Take a matrix \(Y\) representing all of the \((n^2 - n)\) associations between all realizations of the \(Y\) variable in region \(\mathbb{R}\) and \(W\) represents all the \((w^2-w)\) associations of the spatial units to each other in region \(\mathbb{R}\) irrespective of \(Y\). Then the degree to which the two matrices are positively/negatively correlated is the degree of positive/negative spatial autocorrelation.

Consequently, if it is assumed that neighboring spatial units are associated and so are represented in the \(W\) matrix as high positive numbers and low numbers or zeros for all others and the \(Y\) matrix has high values in spatial units neighboring other high values, then the two matrices are similar in structure and positive spatial autocorrelation exists.