Spatial Autoregressive and Network Autocorrelation Models

Wei Lan and Chih-Ling Tsai
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Wei Lan: Southwestern University of Finance and Economics, School of Statistics and Data Science and Center of Statistical Research
Chih-Ling Tsai: University of California - Davis, Graduate School of Management

Chapter Chapter 7 in Covariance Analysis and Beyond, 2026, pp 101-119 from Springer

Abstract: Abstract This chapter introduces the spatial autoregressive modelSpatial autoregressive (SAR) models, which has a specific covariance structure so that it is able to take into account the spatial dependence and heterogeneity of responses by leveraging spatial information. The quasi-maximum likelihood estimationQuasi-maximum likelihood estimation (QMLE) method is employed to estimate unknown parameters. We then allow the adjacency matrix to exhibit network interactions and present two adaptive network autocorrelation modelsNetwork autocorrelation (NAM) models for identifying influential nodes. Furthermore, screening large-scale networks in a network autocorrelation modelNetwork autocorrelation (NAM) models for selecting relevant nodes is discussed. In addition to models with univariate structure, multivariate network autocorrelation modelsMultivariate network autocorrelation model are analyzed. Moreover, four additional types of network autocorrelation modelsNetwork autocorrelation (NAM) models are provided to discuss the mutual influence, functional varying coefficient, quantile, and community effects, respectively. Finally, three examples are given to briefly illustrate empirical applications.

Date: 2026
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DOI: 10.1007/978-3-032-08796-6_7

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