Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models

We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a "pseudo-score" test derived from Besag's pseudo-likelihood, 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 localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.Comment: Published in at http://dx.doi.org/10.1214/11-STS367 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Leverage and influence diagnostics for Gibbs spatial point processes

For point process models fitted to spatial point pattern data, we describe diagnostic quantities analogous to the classical regression diagnostics of leverage and influence. We develop a simple and accessible approach to these diagnostics, and use it to extend previous results for Poisson point process models to the vastly larger class of Gibbs point processes. Explicit expressions, and efficient calculation formulae, are obtained for models fitted by maximum pseudolikelihood, maximum logistic composite likelihood, and regularised composite likelihoods. For practical applications we introduce new graphical tools, and a new diagnostic analogous to the effect measure DFFIT in regression

Efficient Code for Second Order Analysis of Events on a Linear Network

We describe efficient algorithms and open-source code for the second-order statistical analysis of point events on a linear network. Typical summary statistics are adaptations of Ripley's K-function and the pair correlation function to the case of a linear network, with distance measured by the shortest path in the network. Simple implementations consume substantial time and memory. For an efficient implementation, the data structure representing the network must be economical in its use of memory, but must also enable rapid searches to be made. We have developed such an efficient implementation in C with an R interface written as an extension to the R package spatstat. The algorithms handle realistic large networks, as we demonstrate using a database of all road accidents recorded in Western Australia