Stagewise generalized estimating equations with grouped variables

Forward stagewise estimation is a revived slow-brewing approach for model building that is particularly attractive in dealing with complex data structures for both its computational efficiency and its intrinsic connections with penalized estimation. Under the framework of generalized estimating equations, we study general stagewise estimation approaches that can handle clustered data and non-Gaussian/non-linear models in the presence of prior variable grouping structure. As the grouping structure is often not ideal in that even the important groups may contain irrelevant variables, the key is to simultaneously conduct group selection and within-group variable selection, that is, bi-level selection. We propose two approaches to address the challenge. The first is a bi-level stagewise estimating equations (BiSEE) approach, which is shown to correspond to the sparse group lasso penalized regression. The second is a hierarchical stagewise estimating equations (HiSEE) approach to handle more general hierarchical grouping structure, in which each stagewise estimation step itself is executed as a hierarchical selection process based on the grouping structure. Simulation studies show that BiSEE and HiSEE yield competitive model selection and predictive performance compared to existing approaches. We apply the proposed approaches to study the association between the suicide-related hospitalization rates of the 15-19 age group and the characteristics of the school districts in the State of Connecticut.