The role of Spatial Autocorrelation on spatially correlated data for Hierarchical Cluster Analysis - Koutsos, Thomas; Menexes, George (Τετράδια Ανάλυσης Δεδομένων, 2024)
Ordinary multi-variate statistical analyses usually consider only the correlation between variables ignoring the location of the objects-data points. One of the core principles of Statistics is that observations and their corresponding values, either between or within various groups, are independent of each other. The fundamental concept of spatial dependence and spatial autocorrelation is often omitted in ordinary statistical analysis, although coordinates of measurements are usually available. Current study examines the results of two different methodological approaches to test the benefit of considering the “spatial information” of the measurements: (1) Hierarchical Cluster Analysis (HCA) with corrected data (replacement of missing values with sowing row mean value), and (2) Hierarchical Cluster Analysis with data after spatial interpolation applied. Spatial Autocorrelation Analysis (Univariate Local Moran’s I) was used to check the spatial autocorrelation of data in each case via LISA (Local Indicators of Spatial Association–LISA) cluster maps and thus make visual comparisons between the above two methodological schemes. Both HCA analysis and LISA cluster maps show that considering the “spatial” location of the measurements can lead to different results than those from an ordinary statistical analysis without spatial correlated data. Comparing LISA cluster maps to quantile maps (that show the real distribution of data) it can be deduced that considering the spatial information (via spatial interpolation) can lead to results closer to the real distribution of data.