Score, pseudo-score and residual diagnostics for goodness-of-fit of spatial point process models

We develop new tools for formal inference and informalmodel validation in the analysis of spatial point pattern data. The score test is generalised to a ‘pseudo-score’ test derived from Besag’s pseudolikelihood, and to a class of diagnostics based on point process residuals. The results lend theoretical support to the established practice of using functional summary statistics such as Ripley’s K-function, when testing for complete spatial randomness; and they provide new tools such as the compensator of the K-function for testing other fitted models. The results also support localisation methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.