Residual Diagnostics for Covariate Effects in Spatial Point Process Models |
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Authors: | Adrian Baddeley Ya-Mei Chang Yong Song Rolf Turner |
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Institution: | 1. CSIRO Mathematics, Informatics and Statistics , Floreat , Western Australia;2. School of Mathematics &3. Statistics , University of Western Australia , Crawley , Western Australia;4. Department of Statistics , Tamkang University , Taiwan;5. CSIRO Land and Water , Highett , Victoria , Australia;6. Department of Statistics , University of Auckland , New Zealand |
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Abstract: | For a spatial point process model in which the intensity depends on spatial covariates, we develop graphical diagnostics for validating the covariate effect term in the model, and for assessing whether another covariate should be added to the model. The diagnostics are point-process counterparts of the well-known partial residual plots (component-plus-residual plots) and added variable plots for generalized linear models. The new diagnostics can be derived as limits of these classical techniques under increasingly fine discretization, which leads to efficient numerical approximations. The diagnostics can also be recognized as integrals of the point process residuals, enabling us to prove asymptotic results. The diagnostics perform correctly in a simulation experiment. We demonstrate their utility in an application to geological exploration, in which a point pattern of gold deposits is modeled as a point process with intensity depending on the distance to the nearest geological fault. Online supplementary materials include technical proofs, computer code, and results of a simulation study. |
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Keywords: | Added variable plot Component-plus-residual plot Generalized linear models Partial residual plot Point process residuals Spatial covariates |
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