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Estimation and selection for spatial zero‐inflated count models

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  • Chung‐Wei Shen
  • Chun‐Shu Chen

Abstract

The count data arise in many scientific areas. Our concerns here focus on spatial count responses with an excessive number of zeros and a set of available covariates. Estimating model parameters and selecting important covariates for spatial zero‐inflated count models are both essential. Importantly, to alleviate deviations from model assumptions, we propose a spatial zero‐inflated Poisson‐like methodology to model this type of data, which relies only on assumptions for the first two moments of spatial count responses. We then design an effective iterative estimation procedure between the generalized estimating equation and the weighted least squares method to respectively estimate the regression coefficients and the variogram of the data model. Moreover, the stabilization of estimators is evaluated via a block jackknife technique. Furthermore, a distribution‐free model selection criterion based on an estimate of the mean squared error of the estimated mean structure is proposed to select the best subset of covariates. The effectiveness of the proposed methodology is demonstrated by simulation studies under various scenarios, and a real dataset regarding the number of maternal deaths in Mozambique is analyzed for illustration.

Suggested Citation

  • Chung‐Wei Shen & Chun‐Shu Chen, 2024. "Estimation and selection for spatial zero‐inflated count models," Environmetrics, John Wiley & Sons, Ltd., vol. 35(4), June.
    • Handle: RePEc:wly:envmet:v:35:y:2024:i:4:n:e2847
    DOI: 10.1002/env.2847
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    References listed on IDEAS

    as
    1. Wei Pan, 2001. "Akaike's Information Criterion in Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 57(1), pages 120-125, March.
    2. Chung-Wei Shen & Yi-Hau Chen, 2012. "Model Selection for Generalized Estimating Equations Accommodating Dropout Missingness," Biometrics, The International Biometric Society, vol. 68(4), pages 1046-1054, December.
    3. Shen, Xiaotong & Huang, Hsin-Cheng, 2006. "Optimal Model Assessment, Selection, and Combination," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 554-568, June.
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    5. Oyelola A. Adegboye & Denis H. Y. Leung & You‐Gan Wang, 2018. "Analysis of spatial data with a nested correlation structure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(2), pages 329-354, February.
    6. Chun‐Shu Chen & Hong‐Ding Yang & Yang Li, 2014. "A stabilized and versatile spatial prediction method for geostatistical models," Environmetrics, John Wiley & Sons, Ltd., vol. 25(2), pages 127-141, March.
    7. Kong, Maiying & Xu, Sheng & Levy, Steven M. & Datta, Somnath, 2015. "GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 54-66.
    8. Jian Wang & Cielito C. Reyes-Gibby & Sanjay Shete, 2021. "An Approach to Analyze Longitudinal Zero-Inflated Microbiome Count Data Using Two-Stage Mixed Effects Models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 267-290, July.
    9. Osvaldo Loquiha & Niel Hens & Leonardo Chavane & Marleen Temmerman & Nafissa Osman & Christel Faes & Marc Aerts, 2018. "Mapping maternal mortality rate via spatial zero-inflated models for count data: A case study of facility-based maternal deaths from Mozambique," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-21, November.
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