Fig. 1

Four scenarios illustrating a spectrum of possible relations between hard and soft traits: A This non-monotonic relationship allows prediction of the hard trait using the soft one, but not through a simple linear method. B An example of a monotonic relation, where the two traits are linearly related on a portion of their variation domain, only allowing accurate predictions of one trait by the other (either way) on this part. C The traits are here linearly related, but reliable predictions cannot be achieved because of the high standard error. D The ideal linear, strong and monotonic relationship needed for PCA and correlations. Thus, one can use a trait as a proxy for another one only if there is a well-known relationship that is correctly estimated, implying (1) the knowledge of the form of the relationship between the two traits, (2) a relationship where the values of one trait change with the values of the other (i.e. no constant values of one trait as the other one is changing) because such a relation prevents prediction on one of the traits and (3) a standard error on the model parameter small enough to give a reliable prediction