Title: Semi-parametric multinomial logistic regression for multivariate point processes
Authors: Rasmus Waagepetersen - Aalborg University (Denmark) [presenting]
Abstract: Multivariate point pattern data are becoming increasingly common. In ecology for example, biologists collect large data sets of locations of hundred thousands trees belonging to hundreds of species. Similarly, in many major cities, police authorities record locations, times and types of street crimes. We discuss a semi-parametric approach to analysing street crime data where the intensity functions of different types of crime scenes are specified by regression models up to a common unknown spatially varying factor. This factor may e.g. represent variations in crime intensity due to complex urban structures and population density. No restrictive assumptions of independence within or between crime types are imposed. We discuss how inference on the intensity functions can be conducted using a multinomial conditional composite likelihood. In this connection we address how to estimate standard errors of the regression parameter estimates where these standard errors depend on the multivariate dependence structure between the different types of points. We apply the methodology to a data set of street crimes from Washington DC and show how interesting spatial patterns emerge as a result of our analysis.