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The explanation of spatial errors in geospatial modelling has long been a challenge. This study introduces an index that captures the complexity of local spatial distribution, which can partially provide insight into spatial errors. While previous studies have explored the complexity of geographical data from various perspectives, there is limited knowledge on assessing the complexity while taking spatial dependence into account. This study proposes a measure of geocomplexity, i.e. the spatial local complexity indicator, which characterizes the complexity of local spatial patterns while considering spatial neighbor dependence. We used both aspatial and spatial models to estimate the economic inequality in Australia, and applied the spatial local complexity indicator to explain spatial errors in these models. Results show that the developed geocomplexity indicator, using a binary spatial matrix, can effectively explain spatial errors arising from models, including 17%-47% of errors in aspatial models and 14% in a spatial model. The experiments in this study support our hypothesis that geocomplexity is an essential component in explaining spatial errors. The proposed geocomplexity indicator, along with our hypothesis, has the potential for advancing the understanding complex geospatial systems and enabling applications in various fields related to spatial data analysis. [ABSTRACT FROM AUTHOR]

Spatial heterogeneity refers to uneven distributions of geographical variables. Spatial interpolation methods that utilize spatial heterogeneity are sensitive to the way in which spatial heterogeneity is characterized. This study developed a Generalized Heterogeneity Model (GHM) for characterizing local and stratified heterogeneity within variables and to improve interpolation accuracy. GHM first divides a study area into multiple spatial strata according to the sample values and locations of a variable. Then, GHM estimates simultaneously the spatial variations of the variable within and between the spatial strata. Finally, GHM interpolates unbiased estimates and uncertainty at unsampled locations. We demonstrated the GHM by predicting the spatial distributions of marine chlorophyll in Townsville, Queensland, Australia. Results show that GHM improved both the overall interpolation accuracy across the study area and along strata boundaries compared with previous interpolation models. GHM also avoided bull's eye patterns and abrupt changes along strata boundaries. In future studies, GHM has the potential to be integrated with machine learning and advanced algorithms to improve spatial prediction accuracy for studies in broader fields. [ABSTRACT FROM AUTHOR]

Geographical variables are usually not independent of each other. Hence, it is necessary to investigate the effect of interactions among explanatory variables on a response variable to characterize spatially enhanced or weakened relationships among all variables. The geographical detector (GD) model identifies zones for each explanatory variable, divides the study area into spatial units by overlapping these zones, and quantifies spatial associations as the power of interactive determinant (PID) between a response variable and explanatory variables. Consequently, the PID values depend upon the distributions of explanatory variables (i.e. spatial characteristics) and the subsequent division of spatial units out of these explanatory variables. This study has therefore proposed an Interactive Detector for Spatial Associations (IDSA) to optimize spatial division and improve PID. IDSA utilizes spatial autocorrelation of each explanatory variable and optimizes spatial units based on spatial fuzzy overlay to compute PID. We test the IDSA on both a simulation study and practical case that analyzes road deterioration in Australia. Results showed that the IDSA model could effectively assess the PID while existing GD overestimated PID. Hence, the IDSA improves the GD with refined spatial units based on explanatory variables to enhance their local spatial associations with a response variable. [ABSTRACT FROM AUTHOR]