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Spatially clustered varying coefficient model

Author

Listed:
  • Lin, Fangzheng
  • Tang, Yanlin
  • Zhu, Huichen
  • Zhu, Zhongyi

Abstract

In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the regression coefficients are allowed to vary smoothly within each cluster but change abruptly across the boundaries of adjacent clusters, and we develop a unified approach for simultaneous coefficient estimation and cluster identification. The varying coefficients are approximated by penalized splines, and the clusters are identified through a fused concave penalty on differences in neighboring locations, where the spatial neighbors are specified by the minimum spanning tree (MST). The optimization is solved efficiently based on the alternating direction method of multipliers, using the sparsity structure from MST. Furthermore, we establish the oracle property of the proposed method considering the structure of MST. Numerical studies show that the proposed method can efficiently incorporate spatial neighborhood information and automatically detect possible spatially clustered patterns in the regression coefficients. An empirical study in oceanography illustrates that the proposed method is promising to provide informative results.

Suggested Citation

  • Lin, Fangzheng & Tang, Yanlin & Zhu, Huichen & Zhu, Zhongyi, 2022. "Spatially clustered varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jmvana:v:192:y:2022:i:c:s0047259x22000458
    DOI: 10.1016/j.jmva.2022.105023
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    References listed on IDEAS

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    1. Furong Li & Huiyan Sang, 2019. "Spatial Homogeneity Pursuit of Regression Coefficients for Large Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1050-1062, July.
    2. Zhihua Ma & Yishu Xue & Guanyu Hu, 2020. "Heterogeneous regression models for clusters of spatial dependent data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 15(4), pages 459-475, October.
    3. Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
    4. David Wheeler & Lance Waller, 2009. "Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests," Journal of Geographical Systems, Springer, vol. 11(1), pages 1-22, March.
    5. Zhihua Ma & Yishu Xue & Guanyu Hu, 2019. "Heterogeneous Regression Models for Clusters of Spatial Dependent Data," Papers 1907.02212, arXiv.org, revised Apr 2020.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Laura M. Sangalli & James O. Ramsay & Timothy O. Ramsay, 2013. "Spatial spline regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 681-703, September.
    8. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    9. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    11. Haonan Wang & M. Giovanna Ranalli, 2007. "Low-Rank Smoothing Splines on Complicated Domains," Biometrics, The International Biometric Society, vol. 63(1), pages 209-217, March.
    12. Jingru Mu & Guannan Wang & Li Wang, 2020. "Spatial autoregressive partially linear varying coefficient models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(2), pages 428-451, April.
    13. Zudi Lu & Dag Johan Steinskog & Dag Tjøstheim & Qiwei Yao, 2009. "Adaptively varying‐coefficient spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 859-880, September.
    14. Tim Ramsay, 2002. "Spline smoothing over difficult regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 307-319, May.
    15. Simon N. Wood & Mark V. Bravington & Sharon L. Hedley, 2008. "Soap film smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 931-955, November.
    16. Jingru Mu & Guannan Wang & Li Wang, 2018. "Estimation and inference in spatially varying coefficient models," Environmetrics, John Wiley & Sons, Ltd., vol. 29(1), February.
    17. Zheng Tracy Ke & Jianqing Fan & Yichao Wu, 2015. "Homogeneity Pursuit," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 175-194, March.
    18. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    19. Shujie Ma & Jian Huang, 2017. "A Concave Pairwise Fusion Approach to Subgroup Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 410-423, January.
    Full references (including those not matched with items on IDEAS)

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