ABSTRACT
The Local Join Count statistic and Quantile LISA methods extend the notion of univariate and multivariate local spatial autocorrelation statistics beyond continuous variables. The univariate Local Join Count is a local version of the classic join count statistic for spatial autocorrelation for a binary variable. Its extension to a bivariate case distinguishes between a layout where the two variables cannot occur at the same location and one where it can. The former is termed Bivariate Local Join Count in GeoDa, the latter Co-Location Join Count. The extension to multiple binary variables that can co-locate is straightforward, although meaningful occurrences of co-location become rare as the number of variables increases. Inference for these statistics is based on a permutation approach.
The principle behind the Local Join Count statistic is broadened by applying it to a subset of observations on a continuous variable that satisfy a given constraint. The application of this concept to a specific quantile of the distribution leads to the notion of a Quantile LISA. This provides an alternative way to interpret clusters and spatial outliers.
