In multivariate analysis, canonical correspondence analysis (CCA) is an
ordination
Ordination is the process by which individuals are Consecration, consecrated, that is, set apart and elevated from the laity class to the clergy, who are thus then authorization, authorized (usually by the religious denomination, denominational ...
technique that determines axes from the response data as a linear combination of measured predictors. CCA is commonly used in
ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps wi ...
in order to extract gradients that drive the composition of ecological communities. CCA extends
Correspondence Analysis (CA) Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rath ...
with regression, in order to incorporate predictor variables.
History
CCA was developed in 1986 by Cajo ter Braak
and implemented in the program CANOCO, an extension of DECORANA. To date, CCA is one of the most popular multivariate methods in ecology, despite the availability of contemporary alternatives. CCA was originally derived and implemented using an algorithm of weighted averaging, though Legendre & Legendre (1998) derived an alternative algorithm.
Assumptions
The requirements of a CCA are that the samples are random and independent. Also, the data are categorical and that the independent variables are consistent within the sample site and error-free.
[McGarigal, K., S. Cushman, and S. Stafford (2000). ''Multivariate Statistics for Wildlife and Ecology Research''. New York, New York, USA: Springer.] The original publication states the need for equal species tolerances, equal species maxima, and equispaced or uniformly distributed species optima and site scores.
See also
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Canonical correlation analysis
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X'n'') and ''Y' ...
(CANCOR)
References
Dimension reduction
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