Linden & Roloff (2015) - corrigendum

Linden & Roloff (2015) described an approach to specifying a prior variance for regression coefficients that attempted to follow the approach used by Link & Barker (2006). The description and implementation in Linden & Roloff (2015) were incorrect.

Link & Barker (2006) discuss the problems associated with vague priors, and illustrate a simple example where the prior variance has an influence on model selection (Figure 2). We illustrated a similar issue in Figure 5 of Linden & Roloff (2015) where increasing the prior variance to arbitrarily large values for regression coefficients caused the inclusion probabilities to decrease for those parameters that did not have very strong support. The solution presented by Link & Barker (2006) (hereafter, the L&B prior) was to define a total variance (V) for the linear predictor and partition that variance among each regression parameter depending on how many parameters are included in the predictor. Thus, the prior variance for a given parameter is defined as V/(k+1), where k is the number of regression coefficients included in a model, not including the intercept (hence the +1).

Our application of the L&B prior incorrectly partitioned a single variance equally to all parameters from the dynamic multistate model, across multiple linear predictors. If following the logic of Link & Barker (2006) we should have specified multiple variances, one for each of the 5 linear predictors that had regression coefficients with inclusion uncertainty. Additionally, the JAGS code erroneously weighted the inverse variance (tau) instead of the variance.

Applying the correctly specified L&B prior (see corrected Appendix S1) does not significantly alter inferences, with the exception that the mean variance suggested for regression coefficient priors is much smaller than previously reported (see corrected Figure 5). This largely follows the variance indicated by the informed prior. As a result, inclusion probabilities are increased for all parameters with weak to moderate support.