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Statistical Analysis in the Presence of Spatial Autocorrelation: Selected Sampling Strategy Effects

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  • Daniel A. Griffith

    (School of Economic, Political, and Policy Sciences, University of Texas at Dallas, Richardson, TX 75080, USA)

  • Richard E. Plant

    (Departments of Plant Sciences and Biological and Agricultural Engineering, University of California, Davis, CA 95616, USA)

Abstract

Fundamental to most classical data collection sampling theory development is the random drawings assumption requiring that each targeted population member has a known sample selection (i.e., inclusion) probability. Frequently, however, unrestricted random sampling of spatially autocorrelated data is impractical and/or inefficient. Instead, randomly choosing a population subset accounts for its exhibited spatial pattern by utilizing a grid, which often provides improved parameter estimates, such as the geographic landscape mean, at least via its precision. Unfortunately, spatial autocorrelation latent in these data can produce a questionable mean and/or standard error estimate because each sampled population member contains information about its nearby members, a data feature explicitly acknowledged in model-based inference, but ignored in design-based inference. This autocorrelation effect prompted the development of formulae for calculating an effective sample size (i.e., the equivalent number of sample selections from a geographically randomly distributed population that would yield the same sampling error) estimate. Some researchers recently challenged this and other aspects of spatial statistics as being incorrect/invalid/misleading. This paper seeks to address this category of misconceptions, demonstrating that the effective geographic sample size is a valid and useful concept regardless of the inferential basis invoked. Its spatial statistical methodology builds upon the preceding ingredients.

Suggested Citation

  • Daniel A. Griffith & Richard E. Plant, 2022. "Statistical Analysis in the Presence of Spatial Autocorrelation: Selected Sampling Strategy Effects," Stats, MDPI, vol. 5(4), pages 1-20, December.
  • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:81-1353:d:1005774
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    References listed on IDEAS

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    1. Jiahua Chen, 2017. "On finite mixture models," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 15-27, January.
    2. James P. LeSage & R. Kelley Pace, 2014. "The Biggest Myth in Spatial Econometrics," Econometrics, MDPI, vol. 2(4), pages 1-33, December.
    3. Ioulia Papageorgiou, 2016. "Sampling from Correlated Populations: Optimal Strategies and Comparison Study," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 119-151, May.
    4. Acosta, Jonathan & Alegría, Alfredo & Osorio, Felipe & Vallejos, Ronny, 2021. "Assessing the effective sample size for large spatial datasets: A block likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    5. Daniel A. Griffith, 2020. "A Family of Correlated Observations: From Independent to Strongly Interrelated Ones," Stats, MDPI, vol. 3(3), pages 1-19, June.
    6. Hodges, James S. & Reich, Brian J., 2010. "Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You Love," The American Statistician, American Statistical Association, vol. 64(4), pages 325-334.
    7. Ron Johnston & Kelvyn Jones & David Manley, 2018. "Confounding and collinearity in regression analysis: a cautionary tale and an alternative procedure, illustrated by studies of British voting behaviour," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1957-1976, July.
    8. Mark D. Partridge & Marlon Boarnet & Steven Brakman & Gianmarco Ottaviano, 2012. "Introduction: Whither Spatial Econometrics?," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 167-171, May.
    9. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    10. Jon Wakefield, 2003. "Sensitivity Analyses for Ecological Regression," Biometrics, The International Biometric Society, vol. 59(1), pages 9-17, March.
    11. Junyu Zheng & H. Christopher Frey, 2004. "Quantification of Variability and Uncertainty Using Mixture Distributions: Evaluation of Sample Size, Mixing Weights, and Separation Between Components," Risk Analysis, John Wiley & Sons, vol. 24(3), pages 553-571, June.
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    Cited by:

    1. Letícia Ellen Dal Canton & Luciana Pagliosa Carvalho Guedes & Miguel Angel Uribe-Opazo & Tamara Cantu Maltauro, 2023. "Effective Sample Size with the Bivariate Gaussian Common Component Model," Stats, MDPI, vol. 6(4), pages 1-18, October.

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