We develop new tools for formal inference and informal model 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.

AMS 2000 subject classifications: Primary 62M30; secondary 62J20

Key words and phrases: compensator, functional summary statistics,model validation, point process residuals, pseudo-likelihood