Multivariate point pattern data are becoming increasingly common. In ecology for example, biologists collect large data sets of locations of hundred thousands of trees belonging to hundreds of species. Similarly, in many major cities, police authorities record locations, times and types of street crimes. A third example is spatial epidemiological data on occurrences of different genotypes of a virus or bacteria. In this talk we discuss a semi-parametric approach to analyse such data where the intensity functions of different types of points are specified by regression models up to a common unknown spatially varying factor. In the context of street crime this factor may e.g.\ represent variations in crime intensity due to complex urban structures and population density and similar interpretations can be relevant for epidemiological data.

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. These
standard errors depend on the multivariate dependence structure between the different types of points and we do not impose any restrictive assumptions of independence within or between point types. 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.

References

Hessellund, K., Xu, G., Guan, Y., and Waagepetersen R.(2019)
Semi-parametric multinomial logistic regression for multivariate point patterns, under revision.