My research is conducted under the advisement of Rich Gonzalez. Currently, I am working toward building a generalized interaction framework that can accommodate the complex relationships which often exist between variables. This framework would contain the simple “linear by linear” multiplicative interaction model as a special case. It would allow for curvature analysis, in which the curvature of the response surface provides meaningful insight into the data set.
This topic allows for study in many areas of statistics. In designing a framework for widespread multidisciplinary use, interpretation is an important motivation and consideration. Easy-to- understand visualizations of data can support model selection, found through convex analysis and machine learning techniques such as penalized regression. A generalized framework should allow for variable transformations and even the possibility of functional analysis, depending on the type of data. Exploration of results will involve power calculations and insight into designing multi-stage studies.
