hgwrr: an R package for hierarchical and geographically weighted regression

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This paper presents the R package hgwrr, which implements Hierarchical and Geographically Weighted Regression (HGWR). HGWR draws on both Hierarchical Linear Modeling (HLM) and Geographically Weighted Regression (GWR) to enable the discovery and analysis of geographically varying relationships across multiple spatial scales – a topic of long-standing interest to geographers, environmental scientists, and others working with spatial data. Although GWR and HLM are widely used, GWR is not designed for hierarchical data of observations at one scale nested within groups at another more aggregate scale. And it is likely to fail when sample sizes vary significantly between groups, or several group-level variables are introduced. Meanwhile, HLM typically models regression relationships within a bounded, not continuous conceptualization of geographic space, which limits exploration of the geographic variation in those relationships to some “top-level” partitioning of the study area into discrete regions or similar. These restrictions are problematic when, for example, the goal is to model geographically varying relationships and to obtain geographically localized estimates from spatial hierarchical data. Such data are increasingly common and can arise when the detail of what is measured in the data is greater than the detail of where it is measured due to privacy protection, as an example. HGWR is tailored to these goals and data types. Using two-level data, where “samples” nest into “groups,” HGWR permits estimation of globally fixed and geographically varying regression coefficients, as well as inter-group random effects. It also assesses the statistical significance of the geographical variation revealed. Using the package’s simulated dataset and a Wuhan real estate dataset, we demonstrate the theory, usage, and advantages of HGWR, provide R implementation examples, and compare results with conventional GWR and HLM.