Constructing Graphical Models via the Focused Information Criterion

A focused information criterion is developed to estimate undirected graphical models where for each node in the graph a generalized linear model is put forward conditioned upon the other nodes in the graph. The proposed method selects a graph with a small estimated mean squared error for a user-specified focus, which is a function of the parameters in the generalized linear models, by selecting an appropriate model at each node. For situations where the number of nodes is large in comparison with the number of cases, the procedure performs penalized estimation with quadratic approximations to several popular penalties. To show the procedure's applicability and usefulness we have applied it to two datasets involving voting behavior of U.S. senators and to a clinical dataset on psychopathology.