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A multivariate spatial mixture model for areal data: examining regional differences in standardized test scores

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  • Brian Neelon
  • Alan E. Gelfand
  • Marie Lynn Miranda

Abstract

type="main" xml:id="rssc12061-abs-0001"> Motivated by a study exploring geographic disparities in test scores among fourth graders in North Carolina, we develop a multivariate mixture model for the spatial analysis of correlated continuous outcomes. The responses are modelled as a finite mixture of multivariate normal distributions, which accommodates a wide range of marginal response distributions and allows investigators to examine covariate effects within subpopulations of interest. The model has a hierarchical structure incorporating both individual and areal level predictors as well as spatial random effects for each mixture component. Conditional auto-regressive priors on the random effects provide spatial smoothing and allow the shape of the multivariate distribution to vary flexibly across geographic regions. By integrating over this distribution, we obtain region-specific joint, marginal and conditional inferences of interest. We adopt a Bayesian modelling approach and develop an efficient posterior sampling algorithm that relies primarily on closed form full conditionals. Our results show that students in the central and coastal counties of North Carolina demonstrate higher achievement on average than students in the other parts of the state. These findings can be used to guide county level initiatives, such as school-based literacy programmes, to improve elementary education.

Suggested Citation

  • Brian Neelon & Alan E. Gelfand & Marie Lynn Miranda, 2014. "A multivariate spatial mixture model for areal data: examining regional differences in standardized test scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(5), pages 737-761, November.
    • Handle: RePEc:bla:jorssc:v:63:y:2014:i:5:p:737-761
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    File URL: http://hdl.handle.net/10.1111/rssc.2014.63.issue-5
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    1. da Silva, Roberto & Lamb, Luis C. & Barbosa, Marcia C., 2016. "Universality, correlations, and rankings in the Brazilian universities national admission examinations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 295-306.
    2. Deb, Soudeep & Karmakar, Sayar, 2023. "A novel spatio-temporal clustering algorithm with applications on COVID-19 data from the United States," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    3. Simon Mak & Derek Bingham & Yi Lu, 2016. "A regional compound Poisson process for hurricane and tropical storm damage," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 677-703, November.
    4. 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.
    5. Jarno Vanhatalo & Scott D. Foster & Geoffrey R. Hosack, 2021. "Spatiotemporal clustering using Gaussian processes embedded in a mixture model," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.
    6. Carter Allen & Yuzhou Chang & Brian Neelon & Won Chang & Hang J. Kim & Zihai Li & Qin Ma & Dongjun Chung, 2023. "A Bayesian multivariate mixture model for high throughput spatial transcriptomics," Biometrics, The International Biometric Society, vol. 79(3), pages 1775-1787, September.

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