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Open Access Publications from the University of California

Geographically weighted regression for compositional data: An application to the U.S. household income compositions

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This study builds a bridge between the literatures for geographically weighted regression (GWR) and compositional data analysis (CoDA). GWR allows the modeling of spatial heterogeneity in regression models and is increasingly used in various fields. CoDA provides unique and useful tools for compositional data, which are restricted by a constant-sum constraint. Although compositional data are common in many scientific areas, it is not until recently that increasingly sophisticated statistical methods have been deeply investigated. Many types of spatial models based on geostatistics, spatial statistics, and spatial econometrics for compositional data have been proposed. However, there is less attention to both spatial heterogeneity and the constant-sum constraint. In this study, we propose a GWR model for compositional data. This allows us to model spatially varying relationships while considering the constant-sum constraint. We applied this model to analyze household income compositions at the county level in the US. The interpretational usefulness of the results of spatially varying compositional semi-elasticities is empirically performed.

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