PERMANOVA​

• Direct partitioning of multivariate data, based on a resemblance matrix of choice.
• Multi-factorial designs, interactions, fixed or random factors, nested or crossed, asymmetrical.
• Automatically identifies all terms implicit in a given design, with the ability to pool or remove terms.
• Test-statistics constructed based on expectations of mean squares (EMS).
• Permutation algorithms allow multi-level designs and account for other terms in the model.
• Pairwise comparisons and user-specified contrasts.
  Estimation of effect sizes / variance components.
• Distances among centroids reveal salient patterns in factorial structures.
• Unbalanced or unreplicated designs (split plots, randomized blocks, etc.); choose the Type of SS.

PERMDISP

Test the homogeneity of within-group multivariate dispersions on the basis of any resemblance measure.

The perfect complement to PERMANOVA, PERMDISP focuses on variability – how “spread out” the points are – in different groups.

Excellent for studies of ecological beta diversity in natural systems or studies of genetic variation.

DISTLM / dbRDA

Find out how much variation in the multivariate data cloud is explained by one or more explanatory variables.

Dissimilarity-based multivariate multiple regression analysis is complete here with:

• Marginal and sequential permutation tests of individual regressors;
• Variable selection using forward, backward, step-wise or “best” methods;
• Multivariate analogues to information criteria (AIC, AICc, BIC, adjusted R2) for model comparisons;
• Analyse sets of variables in groups or individually;
• Visualise fitted values with dissimilarity-based redundancy analysis (dbRDA) ordination.

CAP

Perform discriminant analysis in the space of a chosen resemblance measure using canonical analysis of principal coordinates (CAP).

Leave-one-out cross-validation gives a statistical measure of the distinctiveness of a priori groups.

Allocate new samples to existing groups, or predict the positions of new samples along continuous gradients.

Excellent for environmental monitoring programs, morphological analyses of characters, or validation of clustering outcomes with new data.

Explore inter-relationships between two sets of variables in Euclidean space or via a dissimilarity measure using a canonical correlation approach.