Each week, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.
Casleton, E.M., Nordman, D.J. and Kaiser, M.S. (2020), Local structure graph models with higher‐order dependence. Can J Statistics. https://doi.org/10.1002/cjs.11573
Graphs consist of a set of nodes representing entities such as people, cell phone towers, companies, or nations. Some of these nodes are connected by edges that represent some type of a relation between nodes such as family relations, shared signal, business interaction, or defense treaties. Local Structure Graph Models (LSGM) are an approach to modeling the probabilities that potential edges between nodes are realized in a manner that allows the presence or absence of some edges to influence the chances that other edges are present or absent. This allows investigators to model the way that, for example, a defense treaty between two nations influences the probability of a similar treaty between two other nations. Currently, however, LSGM can deal with only pairs of potential edges. This paper extends the original presentation of LSGM to include sets of three or more edges that might influence each other, and gives useful parameterizations of the statistical models that allow the incorporation of external factors as covariates and have meaningful interpretations for the actual problems under consideration. The ability to model sets of three edges that impact each other is important in, among other applications, describing the formation of relations in social science problems, a phenomenon called transitivity. Extending the statistical ability to develop models in which the formation of relations among entities impacts the formation of relations among other entities from only groups of two to larger collections expands the areas of application for this recently developed approach to the analysis of networks.