Analyzing multi-scale spatial point patterns in a pyramid modeling framework

ABSTRACT

Many spatial analysis methods suffer from the scaling issue identified as part of the Modifiable Areal Unit Problem (MAUP). This article introduces the Pyramid Model (PM), a hierarchical data framework integrating space and spatial scale in a 3D environment to support multi-scale analysis. The utility of the PM is tested in examining quadrat density and kernel density, which are commonly used measures of point patterns. The two metrics computed from a simulated point set with varying scaling parameters (i.e. quadrats and bandwidths) are represented in the PM. The PM permits examination of the variation of the density metrics computed at all different scales. 3D visualization techniques (e.g. volume display, isosurfaces, and slicing) allow users to observe nested relations between spatial patterns at different scales and understand the scaling issue and MAUP in spatial analysis. A tool with interactive controls is developed to support visual exploration of the internal patterns in the PM. In addition to the point pattern measures, the PM has potential in analyzing other spatial indices, such as spatial autocorrelation indicators, coefficients of regression analysis and accuracy measures of spatial models. The implementation of the PM further advances the development of a multi-scale framework for spatio-temporal analysis.

KEYWORDS:

• MAUP
• multi-scale analysis
• point pattern
• kernel density
• quadrat density
• visualization

Acknowledgments

The authors would like to express their sincere gratitude to the anonymous reviewers and Dr. Eric Delmelle for their constructive feedback, which ultimately improved the quality of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The data and software that support the findings of this study are available with the identifier(s) in a Github repository (https://github.com/qiang-yi/PM).

Additional information

Funding

This article is based on work supported by two research grants from the U.S. National Science Foundation: one under the Methodology, Measurement & Statistics (MMS) Program (Award No. 2102019) and the other under the Coastlines and People (CoPe) Program (Award No. 2052063). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.