Spatio-temporal ANOVA for replicated point patterns

Spatio-temporal point processes stand as a powerful tool to treat mathematically the idea of randomly distributed points with coordinates corresponding to spatial and temporal components. Usually the analysis focuses on finding interaction patterns between points, however, it has not been paid attention to the analysis of patterns for spatio-temporal replicated data.

There are several approaches when treating spatial replicated data that served as a basis for further statistical analysis. But the analysis of spatio-temporal patterns is not yet fully developed, in fact is still in its infancy. Large sets of questions could be answered by analysing the underlying structures of the patterns sets.
We extend the initial analysis of variance for spatial patterns into spatio-temporal patterns. We calculate one functional descriptor of pattern for each subject to investigate departures from completely spatio-temporal random patterns, both between subjects and between groups. The distributions of our main functional pattern descriptor and of our proposed statistical test are unknown. For nonparametric inference, we use a bootstrap procedure in which we resample our data to estimate the null distribution of our statistical test. A simulation study provides evidence of the validity and power of our procedure for bootstrap hypothesis testing in our context. We conclude with an application of our method to an ecological dataset of most abundant tree species in the Barro Colorado Island.