Hypothesis testing: association with (dis)similarity data

Consider the Mantel test to evaluate whether the distances among objects in a matrix of response variables are linearly correlated with a matrix of explanatory variables describing those same objects. Ranked and unranked data may be used.

Procrustes analysis may be used to compare (dis)similarity matrices through ordinations based on the results of a principal coordinate analysis (PCoA) or non-metric dimensional scaling (NMDS). It tests whether the degree of concordance between two (or more) matrices is greater than expected given random inter-matrix associations.Procrustes analysis allows visual inspection of the results.

Distance-based redundancy analysis (db-RDA) may be used to test whether a (dis)similarity matrix calculated from your response data shows linear association to a matrix of (raw or transformed) explanatory data. The (dis)similarity matrix as a whole is evaluated rather than individual response variables.