Essays on space-time interaction tests

Researchers across a variety of fields are often interested in determining if data are of a random nature or if they exhibit patterning which may be the result of some alternative and potentially more interesting process. This dissertation explores a family of statistical methods, i.e. space-time interaction tests, designed to detect structure within three-dimensional event data. These tests, widely employed in the fields of spatial epidemiology, criminology, ecology and beyond, are used to identify synergistic interaction across the spatial and temporal dimensions of a series of events. Exploration is needed to better understand these methods and determine how their results may be affected by data quality problems commonly encountered in their implementation; specifically, how inaccuracy and/or uncertainty in the input data analyzed by the methods may impact subsequent results. Additionally, known shortcomings of the methods must be ameliorated. The contributions of this dissertation are twofold: it develops a more complete understanding of how input data quality problems impact the results of a number of global and local tests of space-time interaction and it formulates an improved version of one global test which accounts for the previously identified problem of population shift bias. A series of simulation experiments reveal the global tests of space-time interaction explored here to be dramatically affected by the aforementioned deficiencies in the quality of the input data. It is shown that in some cases, a conservative degree of these common data problems can completely obscure evidence of space-time interaction and in others create it where it does not exist. Conversely, a local metric of space-time interaction examined here demonstrates a surprising robustness in the face of these same deficiencies. This local metric is revealed to be only minimally affected by the inaccuracies and incompleteness introduced in these experiments. Finally, enhancements to one of the global tests are presented which solve the problem of population shift bias associated with the test and better contextualize and visualize its results, thereby enhancing its utility for practitioners.