A simple method for distinguishing within- versus between-subject effects using mixed models

Here we describe a statistical procedure called within-subject centering (not to be confused with grand-mean centering; e.g. Kreft et al. 1995). This simple technique can be used in mixed models to separate within-subject effects (i.e. phenotypically plastic or facultative behavioural responses) from between-subject effects (i.e. evolutionarily fixed behavioural responses based on the individual or its class). Such a separation is important as it allows us to distinguish between alternative biological hypotheses and prevents us from erroneously generalizing within-subject relationships to between-subject relationships, or vice versa. We claim no originality for this statistical technique, which is commonly used in the social sciences (e.g. Davis et al., 1961, Raudenbush, 1989, Kreft et al., 1995, Snijders and Bosker, 1999; see also van de Pol & Verhulst 2006). However, we offer it as a piece of overlooked statistical methodology that we think is crucial to many researchers in animal behaviour, and in various other areas of biology as well. We illustrate our explanation of the technique with several biological examples and simulated data, but this method is widely applicable and most readers will probably be able to identify appropriate examples from their own research