IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v192y2022ics0047259x22000458.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000458
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.105023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Zhihua Ma & Yishu Xue & Guanyu Hu, 2019. "Heterogeneous Regression Models for Clusters of Spatial Dependent Data," Papers 1907.02212, arXiv.org, revised Apr 2020.
    4. 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.
    5. 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.
    6. Jingru Mu & Guannan Wang & Li Wang, 2018. "Estimation and inference in spatially varying coefficient models," Environmetrics, John Wiley & Sons, Ltd., vol. 29(1), February.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xin Wang & Xin Zhang, 2024. "Scanner: Simultaneously temporal trend and spatial cluster detection for spatial‐temporal data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Xin & Zhu, Zhengyuan & Zhang, Hao Helen, 2023. "Spatial heterogeneity automatic detection and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    2. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Gerhard Tutz & Jan Gertheiss, 2014. "Rating Scales as Predictors—The Old Question of Scale Level and Some Answers," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 357-376, July.
    4. Gerhard Tutz & Margret-Ruth Oelker, 2017. "Modelling Clustered Heterogeneity: Fixed Effects, Random Effects and Mixtures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 204-227, August.
    5. Luc Anselin & Pedro Amaral, 2024. "Endogenous spatial regimes," Journal of Geographical Systems, Springer, vol. 26(2), pages 209-234, April.
    6. Shan Yu & Aaron M. Kusmec & Li Wang & Dan Nettleton, 2023. "Fusion Learning of Functional Linear Regression with Application to Genotype-by-Environment Interaction Studies," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 401-422, September.
    7. 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.
    8. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    9. Ni, Xiao & Zhang, Hao Helen & Zhang, Daowen, 2009. "Automatic model selection for partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2100-2111, October.
    10. Xiao Ni & Daowen Zhang & Hao Helen Zhang, 2010. "Variable Selection for Semiparametric Mixed Models in Longitudinal Studies," Biometrics, The International Biometric Society, vol. 66(1), pages 79-88, March.
    11. Menafoglio, Alessandra & Secchi, Piercesare, 2017. "Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics," European Journal of Operational Research, Elsevier, vol. 258(2), pages 401-410.
    12. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
    13. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    14. Cristiano Varin & Manuela Cattelan & David Firth, 2016. "Statistical modelling of citation exchange between statistics journals," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(1), pages 1-63, January.
    15. Liu, Jingyuan & Sun, Ao & Ke, Yuan, 2024. "A generalized knockoff procedure for FDR control in structural change detection," Journal of Econometrics, Elsevier, vol. 239(2).
    16. Jeon, Jong-June & Kwon, Sunghoon & Choi, Hosik, 2017. "Homogeneity detection for the high-dimensional generalized linear model," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 61-74.
    17. Liu, Jingyuan & Lou, Lejia & Li, Runze, 2018. "Variable selection for partially linear models via partial correlation," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 418-434.
    18. Nott, David J., 2008. "Predictive performance of Dirichlet process shrinkage methods in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3658-3669, March.
    19. Takuma Yoshida, 2019. "Two stage smoothing in additive models with missing covariates," Statistical Papers, Springer, vol. 60(6), pages 1803-1826, December.
    20. Marta Karas & Damian Brzyski & Mario Dzemidzic & Joaquín Goñi & David A. Kareken & Timothy W. Randolph & Jaroslaw Harezlak, 2019. "Brain Connectivity-Informed Regularization Methods for Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 47-90, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:192:y:2022:i:c:s0047259x22000458. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.