S. Doledec et al., MATCHING SPECIES TRAITS TO ENVIRONMENTAL VARIABLES - A NEW 3-TABLE ORDINATION METHOD, Environmental and ecological statistics, 3(2), 1996, pp. 143-166
This paper addresses the question of studying the joint structure of t
hree data tables R, L and Q. In our motivating ecological example, the
central table L is a sites-by-species table that contains the number
of organisms of a set of species that occurs at a set of sites. At the
margins of L are the sites-by-environment data table R and the specie
s-by-trait data table Q. For relating the biological traits of organis
ms to the characteristics of the environment in which they live, we pr
opose a statistical technique called RLQ analysis (R-mode linked to Q-
mode), which consists in the general singular value decomposition of t
he triplet (R(t)D(I)LD(J)Q,D-q,D-p) where D-I, D-J, D-q, D-p are diago
nal weight matrices, which are chosen in relation to the type of data
that is being analyzed (quantitative, qualitative, etc.). In the speci
al case where the central table is analysed by correspondence analysis
, RLQ maximizes the covariance between linear combinations of columns
of R and Q. An example in bird ecology illustrates the potential of th
is method for community ecologists.