PERMANOVA+ add-on

PERMANOVA+ is an add-on package for PRIMER 6. It was produced as a collaborative effort between Marti Anderson (Department of Statistics, University of Auckland, New Zealand) and Ray Gorley & Bob Clarke (PRIMER-E Ltd, Plymouth, UK). It extends the resemblance-based methods of PRIMER to allow the analysis of multivariate (or univariate) data in the context of more complex sampling structures, experimental designs and models. By adopting a more parametric approach it allows

• partitioning variability according to one or more explanatory variables or factors
• measuring or testing interactions among factors (which can only be defined by reference to modelled main effects)
• developing explicitly quantitative models with explanatory, discriminatory or predictive uses

It retains robustness by being totally resemblance and permutation based.

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PERMANOVA - permutational ANOVA/MANOVA

Analyses univariate or multivariate data in response to factors, groups or treatments in an experimental design. PERMANOVA can be used as a better ANOVA/MANOVA. Whereas ANOVA/MANOVA assumes normal distributions and, implicitly, Euclidean distance, PERMANOVA works with any distance measure that is appropriate to the data, and uses permutations to make it distribution free. It carries this generalisation through to include most of the options you would expect from modern ANOVA/MANOVA implementation. For example, new theoretical work allows the handling of complex unbalanced designs, also including covariables.

PERMDISP - homogeneity of dispersions

Tests the homogeneity of multivariate dispersions within groups, on the basis of any resemblance measure. One application is to help in interpreting the results from a PERMANOVA analysis, which makes the implicit assumption (as for ANOVA and ANOSIM) that dispersions are roughly constant across groups.

PCO - principal coordinates analysis

Unconstrained ordination of multivariate data, projection-based (like principal components), but using any chosen resemblance measure.

DistLM - distance-based linear models

Analyses and models the relationship between a multivariate data cloud, and one or more predictor variables, with various options for model selection. As with the other methods here, it is based on a resemblance matrix and uses permutations, rather than the restrictive Euclidean distance and normality assumptions which underlie the standard approach to linear modelling. For example, in ecology, the resemblance matrix commonly describes dissimilarities (or similarities) among a set of samples on the basis of multivariate species abundance data, and interest may lie in modelling the relationship between this data cloud and one or more environmental variables that were measured for the same set of samples.

dbRDA - distance based redundancy analysis

Ordination and visualisation of fitted models (such as from DISTLM)

 

CAP - canonical analysis of principal coordinates

Constrained ordination, discriminating among a priori groups, or predicting values along a gradient. Distance-based canonical correlation.