Identifying and characterizing extrapolation in multivariate response data

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...

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Vydané v:	PloS one Ročník 14; číslo 12; s. e0225715
Hlavní autori:	Bartley, Meridith L., Hanks, Ephraim M., Schliep, Erin M., Soranno, Patricia A., Wagner, Tyler
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States Public Library of Science 05.12.2019 Public Library of Science (PLoS)
Predmet:	Algae Biology and Life Sciences Chlorophyll A - analysis Earth Sciences Ecological monitoring Ecological studies Ecology Ecology and Environmental Sciences Extrapolation Geography Identification methods Lakes Lakes - chemistry Limnology Linear Models Mathematical models Models, Statistical Multivariate Analysis Nitrogen - analysis Nutrients Oceanography Phosphorus - analysis Physical Sciences Predictions Regression analysis Research and Analysis Methods Social Sciences Statistical analysis Statistical models Statistics as Topic Variance Water quality United States > US Missouri Pennsylvania Michigan
ISSN:	1932-6203, 1932-6203
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Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Competing Interests: The authors have declared that no competing interests exist.
ISSN:	1932-6203 1932-6203
DOI:	10.1371/journal.pone.0225715