# Chapter 5 What are “constrained” ordinations?

Described first by Rao (1964), canonical analysis is a generic term that for several types of statistical analyses sharing a common goal, which is to identify the relationship between a multivariate response table (matrix \(Y\), generally describing the species composition of communities) and a multivariate explanatory table (matrix \(X\), generally containing environmental descriptors) by combining ordination and regression concepts.

Canonical analyses allow users to **test ecological hypothesis concerning the environmental drivers of species composition**. Among the diversity of canonical analysis, we will mainly focus here on Redundancy Analysis (RDA).

### References

Rao, C. Radhakrishna. 1964. “The Use and Interpretation of Principal Component Analysis in Applied Research.”

*Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)*26 (4): 329–58. https://www.jstor.org/stable/25049339.