Chapter 5: Canonical analysis of principal coordinates (CAP)
Key references
Method: Anderson & Robinson (2003), Anderson & Willis (2003)
5.1 General description
Key references Method: , CAP is a routine for performing canonical analysis of principal co...
5.2 Rationale (Flea-beetles)
In some cases, we may know that there are differences among some pre-defined groups (for example,...
5.3 Mechanics of CAP
Details of CAP and how it is related to other methods are provided by and . In brief, a classica...
5.4 Discriminant analysis (Poor Knights Islands fish)
We will begin with an example provided by Trevor Willis and Chris Denny (; ), examining temperate...
5.5 Diagnostics
How did the CAP routine choose an appropriate number of PCO axes to use for the above discriminan...
5.6 Cross-validation
The procedure of pulling out one sample at a time and checking the ability of the model to correc...
5.7 Test by permutation (Anderson’s irises)
CAP can be used to test for significant differences among the groups in multivariate space. The t...
5.8 CAP versus PERMANOVA
It might seem confusing that both CAP and PERMANOVA can be used to test for differences among gro...
5.9 Caveats on using CAP (Tikus Island corals)
When using the CAP routine, it should come as no surprise that the hypothesis (usually) is eviden...
5.10 Adding new samples
A new utility of the windows-based version of the CAP routine in PERMANOVA+ is the ability to pla...
5.11 Canonical correlation: single gradient (Fal estuary biota)
So far, the focus has been on hypotheses concerning groups and the use of CAP for discriminant an...
5.12 Canonical correlation: multiple X’s
In some cases, interest lies in finding axes through the cloud of points so as to maximise correl...
5.13 Sphericising variables
It was previously stated that CAP effectively “sphericises” the data clouds as part of the proces...
5.14 CAP versus dbRDA
So, how does CAP differ from dbRDA for relating two sets of variables? First, dbRDA is directiona...
5.15 Comparison of methods using SVD
The relationship between dbRDA and CAP can also be seen if we consider their formulation using si...
5.16 (Hunting spiders)
A study by explored the relationships between two sets of variables: the abundances of hunting s...