Revisting the Join-count Statistic to Assess Spatial Association without Assuming First-order Homogeneity

• Activity Number: 294
• Type: Topic Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Sandor Kabos and Ferenc Csillag*+
• Companies: Eotvos Lorand University and University of Toronto
• Keywords: spatial statistics ; testing for spatial randomness ; stationarity ; environmental applications

Abstract

Characterization of spatial pattern is an increasingly frequent task in geographical, political, epidemiological, ecological analysis. A widely used classical piece of spatial statistics for the assessment of spatial association of nominal data, such as colors on a map, is the 'ordinary' join-count statistic introduced by O. Moran. Since it is based on counting color-neighbor frequencies, it can reject the null hypothesis (of spatial randomness) due to deviations in the first-order parameters (the probabilities of the colors), or the second-order parameters (the probabilities of color neighbors, or autocorrelation), or both. We have developed a generalized join-count statistic (H.Moran), which specifically tests the second-order properties assuming that the (potentially heterogeneous) probabilities of colors are known. The variance calculation for the test statistic accounts for the covariance induced by the connecting edges in the planar graph of sites over which the variables are observed. Using stochastic simulation experiments we show how O. Moran can generate misleading results and we also confirm that the asymptotic Gaussian approximation holds.