Identifying and characterizing extrapolation in multivariate response data.

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