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Abstract:
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Network regression arises in many areas, e.g. empirical economics, computer science and genetics. In this article, we consider a spatial autoregressive (SAR) model for network data %\citep{zaidi2004mobility,fujita2007modeling} where a particular node is regressed on its neighbors. To estimate the parameters of the model we take a two-step approach similar to \cite{lu2018using} who uses generalized estimating equations (GEE) in the quasi-maximum likelihood estimation framework. In the first step, we apply a community detection algorithm to identify the groups (clusters) and use GEE to estimate group specific parameters. In the second step, we propose a global estimator by combining all group specific estimates. Our first step is significantly different since we are determining groups based on a community detection algorithm while \cite{lu2018using} assumes groups are pre-specified based on geographical properties or other researcher defined economic (social) relationships which could hardly happen for network data. We provide theoretical justification of our approach, substantiate it through empirical simulations and finally apply it on a real data.
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