Canoco for Windows 4.5 covers the following multivariate methods:
A. Unconstrained ordination methods -
methods to describe the structure in a single data set:
- principal components analysis (PCA), with various combinations of data standardization by rows and/or by columns (so supporting, among others, PCA on a covariance matrix and PCA on a correlation matrix). A special case is Aitchison's log-ratio PCA for compositional data
- correspondence analysis (CA), also known as reciprocal averaging
- detrended correspondence analysis (DCA), often incorrectly named as DECORANA, after the original program implementing DCA
- principal coordinates analysis (PCO), a classical method of the metric multidimensional scaling
B. Canonical ordination methods -
methods to explain one data set by another data set (ordinations constrained by explanatory variables):
- redundancy analysis (RDA), also called reduced-rank regression, the canonical form of PCA. Special cases are simple and multiple regression, analysis of variance and the log-ratio form of reduced-rank regression
- canonical correspondence analysis (CCA), the canonical form of CA
- detrended canonical correspondence analysis (DCCA), the canonical form of CCA
- canonical variate analysis (CVA), better known as Fisher linear discriminant analysis
- distance-based redundancy analysis (db-RDA), a constrained form of principal coordinates analysis (PCO)
C. Partial ordination methods -
methods to describe the structure in a data set after accounting for variation explained by a second data set (covariable data):
- partial PCA
- partial CA
- partial DCA
D. Partial canonical ordination methods -
methods to explain one data set by another data set after accounting for variation by a third data set (covariable data):
- partial RDA
- partial CCA
- partial DCCA
- partial CVA
For all the listed multivariate methods, you can have a supplementary data set with explanatory variables, that are projected a posteriori into the ordination space to facilitate the interpretation of results.
The statistical significance of the explanatory variables in (partial) canonical methods can be determined by Monte Carlo permutation tests. Explanatory variables can be tested jointly (overall test) or separately after adjusting for other explanatory variables (partial tests). The problem of (auto-)correlation between samples can be overcome by using special permutation schemes. Canoco for Windows has built-in schemes for:
- data from one or more equi-spaced time series, line transects, or rectangular grids of samples
- data originating from repeated measurement designs, Before-After-Control-Impact (BACI design) and
- data from nested and crossed designs with fixed and random factors
Other useful features include forward selection of explanatory variables, and ordination diagnostics on outliers and influential data points.
In addition, the plotting program CanoDraw for Windows contains both elementary and advanced methods for interpreting ordination diagrams. Elementary methods include:
- plotting values of species or explanatory variables in the ordination diagram
- plotting diversity values in the ordination diagram
- plotting samples or species by group symbols
More advanced methods include:
- fitting and plotting species response curves along ordination axes and
- contouring species or explanatory variables in the ordination diagram by:
- generalized linear modelling (e.g. Gaussian response curves/surfaces)
- loess smoothing
- generalized additive modelling (GAM)