Identifying and Characterizing Extrapolation in Multivariate Response Data

• Activity Number: 577 - Statistical Models in Ecology
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Meridith Bartley* and Ephraim Hanks and Tyler Wagner and Erin Schliep and Patricia Soranno
• Companies: Penn State University and Pennsylvania State University and Penn State University and University of Missouri and Michigan State University
• Keywords: extrapolation; multivariate response; classification and regression trees; prediction ; predictive variance ; joint model

Abstract

Extrapolation is making predictions beyond the range of the data used to estimate a statistical model. In ecological studies, it is not always obvious when and where extrapolation occurs. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are more and more common in ecological investigations. In this paper, we extend previous work for identifying extrapolation by examining predictive variance within a univariate setting and applying novel methods to the multivariate case. We illustrate our approach through an analysis of jointly modeled lake nutrients, productivity, and clarity variables in over 7000 inland lakes from across the northeast and Midwest US. In addition, we illustrate novel exploratory approaches for identifying regions of parameter space where extrapolation are more likely to occur using classification and regression trees.