Spatial Autocorrelation and Political Redistricting: A Task for the Uniform Distribution

Literature Cited

• Abonazel, M., Z. Algamal, F. Awwad, and I. Taha. 2022. A new two-parameter estimator for beta regression model: Method, simulation, and application. Frontiers in Applied Mathematics and Statistics 7:780322. doi: 10.3389/fams.2021.780322.
   Google Scholar
• Bartlett, M. 1975. The statistical analysis of spatial pattern. London: Chapman and Hall.
   Google Scholar
• Besag, J. 1974. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society: Series B (Methodological) 36 (2):192–225. doi: 10.1111/j.2517-6161.1974.tb00999.x.
   Web of Science ®Google Scholar
• Besag, J., J. York, and A. Mollié. 1991. Bayesian image restoration with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics 43 (1):1–20. doi: 10.1007/BF00116466.
   Web of Science ®Google Scholar
• Bivand, R., J. Hauke, and T. Kossowski. 2013. Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods. Geographical Analysis 45 (2):150–79. doi: 10.1111/gean.12008.
   Web of Science ®Google Scholar
• Blom, G. 1954. Transformations of the binomial, negative binomial, Poisson and χ2 distributions. Biometrika 41 (3–4):302–16. doi: 10.2307/2332711.
   Web of Science ®Google Scholar
• Burden, S., and D. Steel. 2016. Empirical zoning distributions for small area data. Geographical Analysis 48 (4):373–90. doi: 10.1111/gean.12104.
   Web of Science ®Google Scholar
• Cliff, A., and J. Ord. 1973. Spatial autocorrelation. London: Pion.
   Google Scholar
• Cliff, A., and J. Ord. 1981. Spatial processes. London: Pion.
   Google Scholar
• Cover, B., and D. Niven. 2021. Geographic gerrymandering. Harvard Law & Policy Review 16 (1):159–215.
   Google Scholar
• Danilevicz, I., and R. Ehlers. 2017. BDSAR: A new package on Bregman divergence for Bayesian simultaneous autoregressive models. arXiv:1704.07414. https://arxiv.org/pdf/1704.07414.pdf.
   Google Scholar
• De Oliveira, V., and J. Song. 2008. Bayesian analysis of simultaneous autoregressive models. Sankhyā: The Indian Journal of Statistics Series B 70 (2):323–50.
   Google Scholar
• Ferrari, S., and F. Cribari-Neto. 2004. Beta regression for modelling rates and proportions. Journal of Applied Statistics 31 (7):799–815. doi: 10.1080/0266476042000214501.
   Web of Science ®Google Scholar
• Gelman, A., and J. Hill. 2007. Data analysis using regression and multilevel/hierarchical models. New York: Cambridge University Press.
   Google Scholar
• Goodchild, M. 1986. Spatial autocorrelation. Norwich, UK: GeoBooks.
   Google Scholar
• Griffith, D. 2000. Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra and Its Applications 321 (1–3):95–112. doi: 10.1016/S0024-3795(00)00031-8.
   Web of Science ®Google Scholar
• Griffith, D. 2003. Spatial autocorrelation and spatial filtering: Gaining understanding through theory and scientific visualization. Berlin: Springer-Verlag.
   Google Scholar
• Griffith, D. 2022. Spatial autocorrelation and unorthodox random variables: The uniform distribution. Chilean Journal of Statistics 13 (2):135–55.
   Web of Science ®Google Scholar
• Griffith, D., and J. Paelinck. 2011. Non-standard spatial statistics and spatial econometrics. Berlin: Springer.
   Google Scholar
• Griffith, D., and P. Peres-Neto. 2006. Spatial modeling in ecology: The flexibility of eigenfunction spatial analyses. Ecology 87 (10):2603–13. doi: 10.1890/0012-9658(2006)87[2603:Smietf.[PMC]2.0.co;2]
   PubMed Web of Science ®Google Scholar
• Gronau, Q., H. Singmann, and E.-J. Wagenmakers. 2020. bridgesampling: An R package for estimating normalizing constants. Journal of Statistical Software 92 (10):1–29. doi: 10.18637/jss.v092.i10.
   Web of Science ®Google Scholar
• G’Sell, M. G., S. Wager, A. Chouldechova, and R. Tibshirani. 2016. Sequential selection procedures and false discovery rate control. Journal of the Royal Statistical Society Series B: Statistical Methodology 78 (2):423–44. doi: 10.1111/rssb.12122.
   Web of Science ®Google Scholar
• Hodges, J., and B. Reich. 2010. Adding spatially-correlated errors can mess up the fixed effect you love. The American Statistician 64 (4):325–34. doi: 10.1198/tast.2010.10052.
   Web of Science ®Google Scholar
• Hughes, J., and M. Haran. 2013. Dimension reduction and alleviation of confounding for spatial generalized linear mixed models. Journal of the Royal Statistical Society Series B: Statistical Methodology 75 (1):139–59. doi: 10.1111/j.1467-9868.2012.01041.x.
   Web of Science ®Google Scholar
• Jagerman, D. 1963. The autocorrelation function of a sequence uniformly distributed modulo 1. The Annals of Mathematical Statistics 34 (4):1243–52. https://www.jstor.org/stable/2238334. doi: 10.1214/aoms/1177703859.
   Google Scholar
• Johnson, N., S. Kotz, and N. Balakrishnan. 1994/1995. Continuous univariate distributions. Vols. 1 & 2, 2nd ed. New York: Wiley.
   Google Scholar
• Johnson, N., S. Kotz, and N. Balakrishnan. 2005. Univariate discrete distributions. 3rd ed. New York: Wiley.
   Google Scholar
• Kaiser, M., and N. Cressie. 1997. Modeling Poisson variables with positive spatial dependence. Statistics & Probability Letters 35 (4):423–32. doi: 10.1016/S0167-7152(97)00041-2.
   Web of Science ®Google Scholar
• Leemis, L., and J. McQueston. 2008. Univariate distribution relationships. The American Statistician 62 (1):45–53. doi: 10.1198/000313008X270448.
   Web of Science ®Google Scholar
• Maškarinec, P. 2020. Spatial dimensions of female political participation: Regional perspective of women’s descriptive representation in Czech local councils, 1994–2018. ISPRS International Journal of Geo-Information 9 (12):729–16. doi: 10.3390/ijgi9120729.
   Web of Science ®Google Scholar
• McCullagh, P., and J. Nelder. 1989. Generalized linear models. 2nd ed. London: Chapman & Hall/CRC.
   Google Scholar
• McGhee, E. 2020. Partisan gerrymandering and political science. Annual Review of Political Science 23 (1):171–85. doi: 10.1146/annurev-polisci-060118-045351.
   Google Scholar
• Mészáros, J., N. Solymosi, and F. Speiser. 2007. Spatial distribution of political parties in Hungary 1990–2006. Political Geography 26 (7):804–23. doi: 10.1016/j.polgeo.2007.06.002.
   Web of Science ®Google Scholar
• Meulman, J., A. Van Der Kooij, and W. Heiser. 2004. Principal components analysis with nonlinear optimal scaling transformations for ordinal and nominal data. In Handbook of quantitative methodology for the social sciences, ed. D. Kaplan, 49–70. London: Sage.
   Google Scholar
• Orcutt, M. 2023. How math has changed the shape of gerrymandering. Quanta Magazine, June 1. https://www.quantamagazine.org/how-math-has-changed-the-shape-of-gerrymandering-20230601/.
   Google Scholar
• Peizer, D., and J. Pratt. 1968. A normal approximation for binomial, F, beta, and other common, related tail probabilities, I. Journal of the American Statistical Association 63 (324):1416–56. doi: 10.2307/2285895.
   Web of Science ®Google Scholar
• Plešivčák, M., J. Buček, V. Bačík, and D. Kusendová. 2016. Theoretical and methodological notes on current options related to examination of voting behaviour—The geographical approach. Acta Geographica Universitatis Comenianae 60 (2):151–70.
   Google Scholar
• Pratt, J. 1968. A normal approximation for binomial, F, beta, and other common, related tail probabilities, II. Journal of the American Statistical Association 63 (324):1457–83.
   Web of Science ®Google Scholar
• Stephens, M. 1986. Tests for the uniform distribution. In Goodness-of-fit-techniques, ed. R. D’Agostino, 331–66. London and New York: Routledge.
   Google Scholar
• Tiefelsdorf, M., and D. Griffith. 2007. Semi-parametric filtering of spatial autocorrelation: The eigenvector approach. Environment and Planning A: Economy and Space 39 (5):1193–1221. doi: 10.1068/a37378.
   Web of Science ®Google Scholar
• Van Hala, M., S. Bandyopadhyay, S. Lahiri, and D. Nordman. 2017. On the non-standard distribution of empirical likelihood estimators with spatial data. Journal of Statistical Planning and Inference 187:109–14. doi: 10.1016/j.jspi.2017.02.007.
   Web of Science ®Google Scholar
• Willemain, R., and A. Desautels. 1993. A method to generate autocorrelated uniform random numbers. Journal of Statistical Computation and Simulation 45 (1–2):23–31. doi: 10.1080/00949659308811469.
   Web of Science ®Google Scholar
• Wimmer, G., and G. Altmann. 1999. Thesaurus of univariate discrete probability distributions. Essen, Germany: STAMM Verlag GmbH.
   Google Scholar
• Wong, D. 2009. In The Sage handbook of spatial analysis, ed. A. Fotheringham and P. Rogerson, 105–24. London: Sage.
   Google Scholar
• Wu, P., and A. Combs. 2019. Geographic information system for and against gerrymandering. In Proceedings of the 2019 conference on information systems applied research (CONISAR), ed. B. Ghosh and L. Mew, vol. 21, 5218. Wrightsville Beach, NC: ISCAP. https://iscap.us/proceedings/conisar/2019/pdf/5218.pdf.
   Google Scholar