Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 67, Issue -, Pages 617-651Publisher
WILEY
DOI: 10.1111/j.1467-9868.2005.00519.x
Keywords
Berman's diagnostic; Berman-Turner device; estimating equations; exponential energy marks; generalized linear models; Georgii-Nguyen-Zessin formula; Kernel smoothing; K-function; Ogata residual; Papangelou conditional intensity; Pearson residuals; pseudolikelihood; Q-Q-plots; quadrat counts; residual plots; scan statistic; space-time point processes
Categories
Ask authors/readers for more resources
We define residuals for point process models fitted to spatial point pattern data, and we propose diagnostic plots based on them. The residuals apply to any point process model that has a conditional intensity; the model may exhibit spatial heterogeneity, interpoint interaction and dependence on spatial covariates. Some existing ad hoc methods for model checking (quadrat counts, scan statistic, kernel smoothed intensity and Berman's diagnostic) are recovered as special cases. Diagnostic tools are developed systematically, by using an analogy between our spatial residuals and the usual residuals for (non-spatial) generalized linear models. The conditional intensity lambda plays the role of the mean response. This makes it possible to adapt existing knowledge about model validation for generalized linear models to the spatial point process context, giving recommendations for diagnostic plots. A plot of smoothed residuals against spatial location, or against a spatial covariate, is effective in diagnosing spatial trend or co-variate effects. Q-Q-plots of the residuals are effective in diagnosing interpoint interaction.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available