Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-19
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
We consider two types of spatial symmetry, namely, symmetry in the mixed or shared nearest neighbor (NN) structures.
We use Pielou’s and Dixon’s symmetry tests which are defined using contingency tables based on the NN relationships between the data points.
We generalize these tests to multiple classes and demonstrate that both the asymptotic and exact versions of Pielou’s first type of symmetry test are extremely conservative in rejecting symmetry in the mixed NN structure and hence should be avoided or only the Monte Carlo randomized version should be used.
Under RL, we derive the asymptotic distribution for Dixon’s symmetry test and also observe that the usual independence test seems to be appropriate for Pielou’s second type of test.
Moreover, we apply variants of Fisher’s exact test on the shared NN contingency table for Pielou’s second test and determine the most appropriate version for our setting.
We also consider pairwise and one-versus-rest type tests in post hoc analysis after a significant overall symmetry test.
We investigate the asymptotic properties of the tests, prove their consistency under appropriate null hypotheses, and investigate finite sample performance of them by extensive Monte Carlo simulations.
The methods are illustrated on a real-life ecological data set.
American Psychological Association (APA)
Ceyhan, Elvan. 2014. Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-23.
https://search.emarefa.net/detail/BIM-1050665
Modern Language Association (MLA)
Ceyhan, Elvan. Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations. The Scientific World Journal No. 2014 (2014), pp.1-23.
https://search.emarefa.net/detail/BIM-1050665
American Medical Association (AMA)
Ceyhan, Elvan. Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-23.
https://search.emarefa.net/detail/BIM-1050665
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1050665