Comparison of Indexes of Aggregation and Association for Three-Dimensional Spatial Data Under Three Computational Scenarios

• Activity Number: 85
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ashley E. Askew*+ and Lynne Seymour and Sydney Everhart and Harald Scherm
• Companies: University of Georgia and The University of Georgia and University of Georgia and University of Georgia
• Keywords: Three-Dimensional Spatial Data ; Aggregation ; Association ; Plant Pathology

Abstract

Given a set of points categorized by type, a question that arises is whether there is aggregation for points within each category or an association between categories. We examine a dataset comprised of three-dimensional coordinates for healthy fruit and structures infected by a plant-pathogenic fungus within a peach tree (Prunus persica). To assess how the data compares with what is expected to occur by chance, the points are dispersed about the volume randomly; indices of aggregation and association are computed across the iterations, forming an empirical distribution for comparison against the data.

The analysis utilizes a modification of Ripley's K statistic, based on the neighbors within a search sphere of increasing size centered at each point of interest. An issue arising from this computation is the problem of search spheres extending outside the volume. Here, we examine three strategies: including all search spheres, rejecting any search sphere that extends beyond the volume, and weighting by the intersection of the volumes. Of interest is whether the computationally less intensive methods are sufficient, and we examine the strengths and weaknesses of the three scenarios.