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Statistical analysis of small-area data based on independence, spatial, non-hierarchical, and hierarchical models

Author

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  • Kang, Emily L.
  • Liu, Desheng
  • Cressie, Noel

Abstract

Data associated with spatially contiguous small areas may be modeled via regression on covariates, with error terms that are either independent or are spatially dependent according to which areas are neighbors of each other. But the data may have extra components of variability due to measurement error, which a careful statistical analysis should filter out. The combination of these possibilities leads to four models, three of which are special cases of the fourth: the spatial hierarchical model. A number of new results are developed for the analysis of small-area data: estimation of the measurement-error variance; diagnostics to determine which model fits and predicts better; and a sensitivity analysis to compare an empirical-Bayesian analysis to a Bayesian analysis. A small-area dataset of doctors' prescription amounts per consultation is fitted to all four types of models and used to illustrate the spatial methodology.

Suggested Citation

  • Kang, Emily L. & Liu, Desheng & Cressie, Noel, 2009. "Statistical analysis of small-area data based on independence, spatial, non-hierarchical, and hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3016-3032, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3016-3032
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    Citations

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    Cited by:

    1. Mohammadreza Mohebbi & Rory Wolfe & Andrew Forbes, 2014. "Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach," IJERPH, MDPI, vol. 11(1), pages 1-20, January.
    2. Connor Donegan & Yongwan Chun & Daniel A. Griffith, 2021. "Modeling Community Health with Areal Data: Bayesian Inference with Survey Standard Errors and Spatial Structure," IJERPH, MDPI, vol. 18(13), pages 1-27, June.
    3. Longford, Nicholas T., 2010. "Small area estimation with spatial similarity," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1151-1166, April.
    4. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    5. Thomas Suesse, 2018. "Estimation of spatial autoregressive models with measurement error for large data sets," Computational Statistics, Springer, vol. 33(4), pages 1627-1648, December.
    6. Hang Zhang & Yong Liu & Dongyang Yang & Guanpeng Dong, 2022. "PM 2.5 Concentrations Variability in North China Explored with a Multi-Scale Spatial Random Effect Model," IJERPH, MDPI, vol. 19(17), pages 1-14, August.
    7. Elaheh Torkashvand & Mohammad Jafari Jozani & Mahmoud Torabi, 2017. "Clustering in small area estimation with area level linear mixed models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1253-1279, October.
    8. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.
    9. Esmail Yarali & Firoozeh Rivaz, 2020. "Incorporating covariate information in the covariance structure of misaligned spatial data," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.

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