Measuring Local Spatial Autocorrelation with Data Reliability Information

Local spatial autocorrelation (SA) measures have been used in exploratory spatial data analysis, particularly in detecting spatial clusters. Existing local SA measures, however, are likely unreliable and biased because they compare only estimates among neighboring spatial units, ignoring errors associated with these estimates. The spatial Bhattacharyya coefficient (SBC) compares probability distributions by considering both estimates and their standard errors. Therefore, it was proposed to be a global SA measure. This article argues that the local version of SBC can serve as a local SA statistic, addressing the deficiency of existing local SA statistics that fail to consider estimate error in their formulations. Significance tests for local SBC are conducted under conditional and total randomization assumptions by using a generalized randomization approach. Simulation experiments and empirical analyses of American Community Survey data show that local SBC complements traditional local SA measures by incorporating data reliability information of estimates in SA assessment. This study shows that the direct comparison of estimate distributions in neighboring units in local SBC is more similar to the comparison of neighboring estimates in local Geary than to the comparison of mean deviations in local Moran. Thus, local SBC can effectively detect zonal boundaries.