Chapter 3: Principal c... | PRIMER-e Learning Hub

3.1 General description

Key references Method: , PCO is a routine for performing principal coordinates analysis () ...

3.2 Rationale

It is difficult to visualise patterns in the responses of whole sets of variables simultaneously....

3.3 Mechanics of PCO

To construct axes that maximise fitted variation (or minimise residual variation) in the cloud of...

3.4 Example: Victorian avifauna

As an example, consider the data on Victorian avifauna at the level of individual surveys, in the...

3.5 Negative eigenvalues

The sharp-sighted will have noticed a conundrum in the output given for the Victorian avifauna sh...

3.6 Vector overlays

A new feature of the PERMANOVA+ add-on package is the ability to add vector overlays onto graphic...

3.7 PCO versus PCA (Clyde environmental data)

Principal components analysis (PCA) is described in detail in chapter 4 of . As stated earlier, P...

3.8 Distances among centroids (Okura macrofauna)

In chapter 1, the difficulty in calculating centroids for non-Euclidean resemblance measures was ...

3.9 PCO versus MDS

We recommend that, for routine ordination to visualise multivariate data on the basis of a chosen...

0.1 Title page

0.2 Contact details and installation of the PERMANOVA+ software

0.3 Introduction to the methods of PERMANOVA+

0.4 Changes from DOS to PERMANOVA+ for PRIMER

0.5 Using this manual

1.1 General description

1.2 Partitioning

1.3 Huygens’ theorem

1.4 Sums of squares from a distance matrix

1.5 The pseudo-F statistic

1.6 Test by permutation

1.7 Assumptions

1.8 One-way example (Ekofisk oil-field macrofauna)

1.9 Creating a design file

1.10 Running PERMANOVA

1.11 Pair-wise comparisons

1.12 Monte Carlo P-values (Victorian avifauna)

1.13 PERMANOVA versus ANOSIM

1.14 Two-way crossed design (Subtidal epibiota)

1.15 Interpreting interactions

1.16 Additivity

1.17 Methods of permutations

1.18 Additional assumptions

1.19 Contrasts

1.20 Fixed vs random factors (Tasmanian meiofauna)

1.21 Components of variation

1.22 Expected mean squares (EMS)

1.23 Constructing $F$ from EMS

1.24 Exchangeable units

1.25 Inference space and power

1.26 Testing the design

1.27 Nested design (Holdfast invertebrates)

1.28 Estimating components of variation

1.29 Pooling or excluding terms

1.30 Designs that lack replication (Plankton net study)

1.31 Split-plot designs (Woodstock plants)

1.32 Repeated measures (Victorian avifauna, revisited)

1.33 Unbalanced designs

1.34 Types of sums of squares (Birds from Borneo)

1.35 Designs with covariates (Holdfast invertebrates, revisited)

1.36 Linear combinations of mean squares (NZ fish assemblages)

1.37 Asymmetrical designs (Mediterranean molluscs)

1.38 Environmental impacts

2.1 General description

2.2 Rationale

2.3 Multivariate Levene’s test (Bumpus’ sparrows)

2.4 Generalisation to dissimilarities

2.5 $P$-values by permutation

2.6 Test based on medians

2.7 Ecological example (Tikus Island corals)

2.8 Choice of measure

2.9 Dispersion as beta diversity (Norwegian macrofauna)

2.10 Small sample sizes

2.11 Dispersion in nested designs (Okura macrofauna)

2.12 Dispersion in crossed designs (Cryptic fish)

2.13 Concluding remarks

3.1 General description

3.2 Rationale

3.3 Mechanics of PCO

3.4 Example: Victorian avifauna

3.5 Negative eigenvalues

3.6 Vector overlays

3.7 PCO versus PCA (Clyde environmental data)

3.8 Distances among centroids (Okura macrofauna)

3.9 PCO versus MDS

4.1 General description

4.2 Rationale

4.3 Partitioning

4.4 Simple linear regression (Clyde macrofauna)

4.5 Conditional tests

4.6 (Holdfast invertebrates)

4.7 Assumptions & diagnostics

4.8 Building models

4.9 Cautionary notes

4.10 (Ekofisk macrofauna)

4.11 Visualising models: dbRDA

4.12 Vector overlays in dbRDA

4.13 dbRDA plot for Ekofisk

4.14 Analysing variables in sets (Thau lagoon bacteria)

4.15 Categorical predictor variables (Oribatid mites)