Identifying and characterizing extrapolation in multivariate response data

Autoři: Meridith L. Bartley aff001;  Ephraim M. Hanks aff001;  Erin M. Schliep aff002;  Patricia A. Soranno aff003;  Tyler Wagner aff004
Působiště autorů: Department of Statistics, Pennsylvania State University, University Park, Pennsylvania, United States of America aff001;  Department of Statistics, University of Missouri, Columbia, Missouri, United States of America aff002;  Department of Fisheries and Wildlife, Michigan State University, East Lansing, Michigan, United States of America aff003;  U.S. Geological Survey, Pennsylvania Cooperative Fish and Wildlife Research Unit, Pennsylvania State University, University Park, Pennsylvania, United States of America aff004
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
prolekare.web.journal.doi_sk: 10.1371/journal.pone.0225715


Faced with limitations in data availability, funding, and time constraints, ecologists are often tasked with making predictions beyond the range of their data. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the data. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are common in ecological investigations. In this paper, we extend previous work that identified extrapolation by applying the predictive variance from the univariate setting to the multivariate case. We propose using the trace or determinant of the predictive variance matrix to obtain a scalar value measure that, when paired with a selected cutoff value, allows for delineation between prediction and extrapolation. We illustrate our approach through an analysis of jointly modeled lake nutrients and indicators of algal biomass and water clarity in over 7000 inland lakes from across the Northeast and Mid-west US. In addition, we outline novel exploratory approaches for identifying regions of covariate space where extrapolation is more likely to occur using classification and regression trees. The use of our Multivariate Predictive Variance (MVPV) measures and multiple cutoff values when exploring the validity of predictions made from multivariate statistical models can help guide ecological inferences.

Klíčová slova:

Conditioned response – Covariance – Eutrophication – Extrapolation – Lakes – Probability distribution – Water quality


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Článok vyšiel v časopise


2019 Číslo 12