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A Spatial Logistic Regression Model Based on a Valid Skew-Gaussian Latent Field

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  • Vahid Tadayon

    (Higher Education Center of Eghlid)

  • Mohammad Mehdi Saber

    (Higher Education Center of Eghlid)

Abstract

Logistic regression is commonly used to estimate the association of one (or more) independent variable(s) with a binary- dependent outcome. In many applications latent sources are both spatially dependent and non-Gaussian; thus, it is desirable to exploit both properties jointly. Spatial logistic regression is a well-established technique of including spatial dependence in logistic regression models. In this paper, we develop a spatial logistic regression model based on a valid skew-Gaussian random field. For parameter estimation, we use a Monte Carlo extension of the EM algorithm along with an approximation based on the standard logistic function. A simulation study is applied in order to determine the performance of the proposed model and also to compare the results with a recently introduced model with established efficiency. The identifiability of the parameters is investigated as well. As an illustrative purpose, an application to the Meuse heavy metals dataset is presented. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Vahid Tadayon & Mohammad Mehdi Saber, 2023. "A Spatial Logistic Regression Model Based on a Valid Skew-Gaussian Latent Field," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 59-73, March.
    • Handle: RePEc:spr:jagbes:v:28:y:2023:i:1:d:10.1007_s13253-022-00512-3
    DOI: 10.1007/s13253-022-00512-3
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    References listed on IDEAS

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    1. Peter J. Diggle & Emanuele Giorgi, 2016. "Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1096-1120, July.
    2. Paciorek, Christopher J., 2007. "Computational techniques for spatial logistic regression with large data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3631-3653, May.
    3. Hosseini, Fatemeh & Eidsvik, Jo & Mohammadzadeh, Mohsen, 2011. "Approximate Bayesian inference in spatial GLMM with skew normal latent variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1791-1806, April.
    4. Won Chang & Murali Haran & Patrick Applegate & David Pollard, 2016. "Calibrating an Ice Sheet Model Using High-Dimensional Binary Spatial Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 57-72, March.
    5. Vahid Tadayon & Abdolrahman Rasekh, 2019. "Non-Gaussian Covariate-Dependent Spatial Measurement Error Model for Analyzing Big Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 49-72, March.
    6. Mahmoudian, Behzad, 2018. "On the existence of some skew-Gaussian random field models," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 331-335.
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