Principal Component and Correspondence Analyses with Respect to Instrumental Variables : An Overview of Their Role in Studies of Structure - Activity and Species - Environment Relationships

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Empirical studies of Structure - Activity Relationships (SAR, see, e.g., Doré and Miquel, 1981, Devillers and Karcher, 1990) and of Species - Environment Relationships (SER, see, e.g., Lebreton and Yoccoz, 1987, Jongman et al., 1987) share several striking characteristics. In both cases, one wishes to link the information in a first table X1 (Activity data, Species data) to the information in a second table X2 (Structure, Environment) obtained on the same statistical units as X1. X2 is supposed to influence X1. As a consequence any statistical approach should take account of this fundamental dissymmetry and should attempt to predict features in X1 from features in X2.