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Documents authored by Timmerman, Richard

Document
Short Paper
DOI: 10.4230/LIPIcs.GIScience.2023.39
A Hierarchical and Geographically Weighted Regression Model and Its Backfitting Maximum Likelihood Estimator (Short Paper)

Authors: Yigong Hu, Richard Harris, Richard Timmerman, and Binbin Lu

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
Spatial heterogeneity is a typical and common form of spatial effect. Geographically weighted regression (GWR) and its extensions are important local modeling techniques for exploring spatial heterogeneity. However, when dealing with spatial data sampled at a micro-level but the geographical locations of them are only known at a higher level, GWR-based models encounter several problems, such as difficulty in establishing the bandwidth. Because data with this characteristic exhibit spatial hierarchical structures, such data can be suitably handled using hierarchical linear modeling (HLM). This model calibrates random effects for sample-level variables in each group to address spatial heterogeneity. However, it does not work when exploring spatial heterogeneity in some group-level variables when there is insufficient variance in each group. In this study, we therefore propose a hierarchical and geographically weighted regression (HGWR) model, together with a back-fitting maximum likelihood estimator, that can be applied to examine spatial heterogeneity in the regression relationships of data where observations nest into high-order groupings and share the same or very close coordinates within those groups. The HGWR model divides coefficients into three types: local fixed effects, global fixed effects, and random effects. Results of a simulation experiment show that HGWR distinguishes local fixed effects from others and also global effects from random effects. Spatial heterogeneity is reflected in the estimates of local fixed effects, along with the spatial hierarchical structure. Compared with GWR and HLM, HGWR produces estimates with the lowest deviations of coefficient estimates. Thus, the ability of HGWR to tackle both spatial and group-level heterogeneity simultaneously suggests its potential as a promising data modeling tool for handling the increasingly common occurrence where data, in secure settings for example, remove the specific geographic identifiers of individuals and release their locations only at a group level.
Cite as

Yigong Hu, Richard Harris, Richard Timmerman, and Binbin Lu. A Hierarchical and Geographically Weighted Regression Model and Its Backfitting Maximum Likelihood Estimator (Short Paper). In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 39:1-39:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hu_et_al:LIPIcs.GIScience.2023.39,
  author =	{Hu, Yigong and Harris, Richard and Timmerman, Richard and Lu, Binbin},
  title =	{{A Hierarchical and Geographically Weighted Regression Model and Its Backfitting Maximum Likelihood Estimator}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{39:1--39:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.39},
  URN =		{urn:nbn:de:0030-drops-189342},
  doi =		{10.4230/LIPIcs.GIScience.2023.39},
  annote =	{Keywords: spatial modelling, hierarchical data, spatial heterogeneity, geographically weighted regression}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.GIScience.2023.40
Introducing a General Framework for Locally Weighted Spatial Modelling Based on Density Regression (Short Paper)

Authors: Yigong Hu, Binbin Lu, Richard Harris, and Richard Timmerman

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
Traditional geographically weighted regression and its extensions are important methods in the analysis of spatial heterogeneity. However, they are based on distance metrics and kernel functions compressing differences in multidimensional coordinates into one-dimensional values, which rarely consider anisotropy and employ inconsistent definitions of distance in spatio-temporal data or spatial line data (for example). This article proposes a general framework for locally weighted spatial modelling to overcome the drawbacks of existing models using geographically weighted schemes. Underpinning it is a multi-dimensional weighting scheme based on density regression that can be applied to data in any space and is not limited to geographic distance.
Cite as

Yigong Hu, Binbin Lu, Richard Harris, and Richard Timmerman. Introducing a General Framework for Locally Weighted Spatial Modelling Based on Density Regression (Short Paper). In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 40:1-40:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{hu_et_al:LIPIcs.GIScience.2023.40,
  author =	{Hu, Yigong and Lu, Binbin and Harris, Richard and Timmerman, Richard},
  title =	{{Introducing a General Framework for Locally Weighted Spatial Modelling Based on Density Regression}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{40:1--40:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.40},
  URN =		{urn:nbn:de:0030-drops-189354},
  doi =		{10.4230/LIPIcs.GIScience.2023.40},
  annote =	{Keywords: Spatial heterogeneity, Multidimensional space, Density regression, Spatial statistics}
}
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