Appendix A. Model selection.
To perform model selection, we undertook a Bayesian procedure (see O’Hara and Sillanpää (2009) for a review). We calculated posterior model probabilities using the method developed by Kuo and Mallick (1998) (see Royle (2008) for an example of implementation in the CR framework). For each parameter for which we wanted to test the relevance, we introduced an indicator variable w having a Bernoulli(0.5) prior distribution, and premultiplied the parameter by w. We computed the posterior model probability for a particular model from the MCMC histories, using the ratio between the number of iterations giving this model over the total number of iterations. We also reported the relative importance of a particular factor by calculating the number of iterations giving a model containing the corresponding parameter over the total number of iterations.
We paid a particular attention to the influence of priors on parameters and their effects on model selection by conducting a sensitivity analysis. As advocated by Link and Barker (2006), we used two priors for the regression parameters, a N(0, 1000) and a N(0, V/np) where np is the number of regression parameters and V has prior Γ-1(0.001, 0.001). There were only minimal changes on posterior results; in particular, the relative importance of covariates was unaffected in both examples.
LITERATURE CITED
Kuo, L. and B. Mallick. 1998. Variable selection for regression models. Sankhya Series B, 60:65–81.
Link, W. A. and R. J. Barker. 2006. Model weights and the foundations of multi-model inference. Ecology, 87:2626–2635.
O’Hara, R. and M. Sillanp¨a¨a. 2009. A review of bayesian variable selection methods: what, how, and which. Bayesian Analysis, 4:85–118.
Royle, J. 2008. Modeling individual effects in the Cormack–Jolly–Seber model: a state–space formulation. Biometrics, 64:364–370.