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Residual analysis for spatial point processes (with discussion) |
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| Authors: | A Baddeley R Turner J Møller M Hazelton |
| Institution: | University of Western Australia, Perth, Australia; University of New Brunswick, Fredericton, Canada; University of Aalborg, Denmark; University of Western Australia, Perth, Australia |
| Abstract: | Summary. 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 λ 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. |
| 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 |