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Abstract:
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A model for vertex attribute data should capture information from both the connectivity in the network and relevant covariates. The covariate effects may not be homogeneous across the network, and in many applications, it is of interest to understand if and how these effects vary. Motivated by better understanding spatial patterns such as these, we consider a statistical model for a process defined on a network that allows the model coefficients to vary smoothly across the network. Leveraging ideas from functional data analysis, our proposed solution consists of a generalized linear model with vertex-indexed covariates and a basis expansion of their coefficients. We employ a regularization procedure cast as a prior distribution on the regression coefficients under a Bayesian setup, so that the predicted responses vary smoothly according to the connectivity of the network. We introduce a novel variable selection procedure and demonstrate the flexibility of our proposed modeling structure. When our outlined methodology is applied to recent crime data from Boston, MA, the model provides insight into the spatial network patterns of residential burglary in the city.
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