Focused information criteria for model selection - a Bayesian perspective

Most model selection criteria, such as Akaike's Information Criterion or Widely Applicable Information Criterion are based on a global measure of out of sample prediction accuracy for the responses. But such criteria may not do a good job when interest is in a particular aspect of the model such as a particular model parameter. The Focused Information Criterion is a model selection tool that has been suggested for this purpose in a frequentist context. It is a measure of the mean square error of the focus parameters, which is then used for model selection. Here we look at its Bayesian analog, the Bayesian Focused Information Criterion, where we use the posterior distribution of the focus parameter(s) to estimate its mean square error. We illustrate our proposed model selection criteria on a longitudinal growth data set of newborns with the goal to study differences in BMI trajectory development among different birth weight classes. We use the average BMI at one year age for the different subgroups as the focus parameter and use it to choose an appropriate model that addresses the research question.