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Summary statistics for measuring the relationship among three types of points in multivariate point patterns

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  • Wu, Liu-Cang
  • Li, Hui-Qiong

Abstract

In multivariate spatial point patterns' statistical analysis, conventional summary statistics can only detect the dependence between two types of points, and cannot be used to detect the dependence among three types of points. New summary statistics are proposed which can be used to detect the influence of the presence the kth type points on the relationship between the ith and the jth type points when the relationship between the ith and the jth type points is positive correlation (or negative correlation, or no spatial interaction), can also be used to infer information about the type of correlation and the range of interaction in multivariate point patterns. In order to reduce the edge-effects the border method to estimate the proposed summary statistics is applied. A simulation and a real example are used to illustrate the proposed methodologies.

Suggested Citation

  • Wu, Liu-Cang & Li, Hui-Qiong, 2009. "Summary statistics for measuring the relationship among three types of points in multivariate point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2809-2816, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:2809-2816
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    1. M. Lieshout, 2006. "A J-Function for Marked Point Patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 235-259, June.
    2. M. N. M. Van Lieshout & A. J. Baddeley, 1999. "Indices of Dependence Between Types in Multivariate Point Patterns," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 511-532, December.
    3. K. Schladitz & A. J. Baddeley, 2000. "A Third Order Point Process Characteristic," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 657-671, December.
    4. M. N. M. van Lieshout & A. J. Baddeley, 1996. "A nonparametric measure of spatial interaction in point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 50(3), pages 344-361, November.
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    1. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.

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