Abstract

For Bayesian hierarchical models represented by directed acyclic graphs, all neighbours of a node provide, potentially conflicting, information on the node. Hence identifying potential conflict between these different information sources can be important for assessing the adequacy of Bayesian hierarchical models. Building on this idea originating from [1], [3] constructed node based conflict measures that have been shown to be well calibrated. Sharing the idea of considering potential conflict between separate information sources for each node, [4] constructed a graphical diagnostic lcp. This can be used both to identify conflict at each node, and provide insight into the nature of the conflict, hence being more informative than summary diagnostics. We link these two ideas together by constructing a new diagnostic plot iic-lcp that is supplementary to lcp, but builds on the framework of [3]. It has the advantage over the lcp with the possibility to display curves corresponding to different parameters in the same plot, saving space and easing comparisons, particularly useful for sets of parameters representing exchangeable groups. We show how to visually read some of the conflict measures defined in [3] from iic-lcp, combining graphical and summary diagnostics.