The trouble with stress: A flexible method for the evaluation of nonmetric multidimensional scaling

Abstract

Nonmetric multidimensional scaling (NMDS) is a powerful statistical tool which enables complex multivariate data sets to be visualized in a reduced number of dimensions. Users typically evaluate the fit of an NMDS ordination via ordination “stress” (i.e., data distortion) against a commonly accepted set of heuristic guidelines. However, these guidelines do not account for the mathematical relationship which links ordination stress to sample size. Consequently, researchers working with large data sets may unnecessarily present ordinations in an intractable number of dimensions, subdivide their data, or forego the use of NMDS entirely and lose the benefits of this highly flexible and useful technique. In order to overcome the limitations of these practices, we advocate for an alternative approach to the evaluation of NMDS ordination fit via the usage of permutation-based ecological null models. We present the rationale for this approach from a theoretical basis, supported by a brief literature review, and an example usage of the methodology. Our literature review shows that NMDS analyses often far exceed the number of observations under which the original stress guidelines were formulated—with a significant increasing trend in recent decades. Adoption of a permutation-based approach will consequently provide a more flexible and quantitative evaluation of NMDS fit and allow for the continued application of NMDS in an era of increasingly large datasets.