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Abstract : |
One impediment to the statistical analysis of network data has been the difficulty in modeling the dependence among the observations. In the very simple case of binary (0-1) network data, some researchers have parameterized network dependence in terms of exponential family representations. Accurate parameter estimation for such models is quite difficult, and the most commonly used models often display a significant lack of fit. Additionally, such models are generally limited to binary data. In contrast, random effects models have been a widely successful tool in capturing statistical dependence for a variety of data types, and allow for prediction, imputation, and hypothesis testing within a general regression context. We propose novel random effects structures to capture network dependence, which can also provide graphical representations of network structure and variability. 1 Network Dependence Network data typically consist of a set of n nodes and a relational tie yi,j, measured on each ordered pair of nodes i, j = 1,..., n. This framework has many applications, including the study of war, trade, the behavior of epidemics, the interconnectedness of the World Wide, |
