Dr. Petrutza Caragea (Department of Statistics, Iowa State University)

Title: Centering for the Autologistic Model

Abstract: An issue that arises in a number of environmental monitoring situations is that of detecting and modeling changes in the structure of the underlying scientific processes that govern the observable phenomena of interest. Ideally, a statistical model used in this type of situation contains parameter values, for which we can assess, for example, changes over time, that correspond to components of the underlying scientific process in an interpretable manner. A traditional approach is to consider the overall level of a process, possibly adjusted by the influence of covariates, to be appropriately modeled as what is called the large-scale model component. When the response variable is binary, a typical approach is to use the logistic automodel. We demonstrate that the traditional parametrization given to autologistic models does not result in concordance of large-scale model structure and marginal data structure and we propose an alternative parametrization that overcomes this difficulty. Several examples of data on the spread of invasive plant species and forest monitoring are used as illustration and motivation for an extension to bivariate autologistic models.