Hierarchical Graphical Models

There is continued debate regarding the exact relation between lower cholesterol levels and increased respiratory disease mortality. One of the goals of this study is to reveal the relationship between subcomponents of cholesterol and pulmonary function. We consider the subcomponents of total cholesterol, namely high-density lipoprotein cholesterol and low-density lipoprotein cholesterol, to investigate the relationship of cholesterol levels with pulmonary function in a longitudinal study. To answer these questions, we propose new methodology for hierarchical reciprocal graphical models. We consider the identification and estimation of these models, and propose maximum likelihood estimation using a generalized EM algorithm. A simulation study of the algorithm and the corresponding estimates reveals excellent performance of the proposed procedures. Application of this methodology to the Normative Aging Study reveals complicated associations between pulmonary function and the subcomponents of total cholesterol.