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Bayesian analysis of partially linear, single-index, spatial autoregressive models

Author

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  • Zhiyong Chen

    (Fujian Normal University
    Fujian Provincial Engineering Technology Research Center for Public Service)

  • Jianbao Chen

    (Fujian Normal University
    Fujian Provincial Engineering Technology Research Center for Public Service)

Abstract

The partially linear single-index spatial autoregressive models (PLSISARM) can be used to evaluate the linear and nonlinear effects of covariates on the response for spatial dependent data. With the nonparametric function approximated by free-knot splines, we develop a Bayesian sampling-based method which can be performed by facilitating efficient Markov chain Monte Carlo approach to analyze PLSISARM and design a Gibbs sampler to explore the joint posterior distributions. To obtain a rapidly-convergent algorithm, we improve the movement step of Bayesian splines with free-knots so that all the knots can be relocated each time instead of only one knot. We illustrate the performance of the proposed model and estimation method by a simulation study and analysis of a Boston housing price dataset.

Suggested Citation

  • Zhiyong Chen & Jianbao Chen, 2022. "Bayesian analysis of partially linear, single-index, spatial autoregressive models," Computational Statistics, Springer, vol. 37(1), pages 327-353, March.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:1:d:10.1007_s00180-021-01123-1
    DOI: 10.1007/s00180-021-01123-1
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    References listed on IDEAS

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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Roberto Basile, 2008. "Regional economic growth in Europe: A semiparametric spatial dependence approach," Papers in Regional Science, Wiley Blackwell, vol. 87(4), pages 527-544, November.
    3. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    4. Olivier Parent & James Lesage, 2005. "Bayesian Model Averaging for Spatial Econometric Models," Post-Print hal-00375489, HAL.
    5. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.
    6. Philipp Piribauer & Jesús Crespo Cuaresma, 2016. "Bayesian Variable Selection in Spatial Autoregressive Models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 11(4), pages 457-479, October.
    7. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2015. "Quantile regression and variable selection of partial linear single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 375-409, April.
    8. C. C. Holmes & B. K. Mallick, 2001. "Bayesian regression with multivariate linear splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 3-17.
    9. James P. Lesage, 1997. "Bayesian Estimation of Spatial Autoregressive Models," International Regional Science Review, , vol. 20(1-2), pages 113-129, April.
    10. Krisztin, Tamás, 2018. "Semi-parametric spatial autoregressive models in freight generation modeling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 121-143.
    11. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    12. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    13. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    14. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    15. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    16. Roberto Basile, 2009. "Productivity Polarization across Regions in Europe," International Regional Science Review, , vol. 32(1), pages 92-115, January.
    17. James P. LeSage & R. Kelley Pace, 2018. "Spatial econometric Monte Carlo studies: raising the bar," Empirical Economics, Springer, vol. 55(1), pages 17-34, August.
    18. Yan Sun & Yueqin Wu, 2018. "Estimation and testing for a partially linear single-index spatial regression model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(4), pages 473-489, October.
    19. Roberto BASILE & Bernard GRESS, 2005. "Semi-Parametric Spatial Auto-Covariance Models Of Regional Growth In Europe," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 21, pages 93-118.
    20. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    21. Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
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