IDEAS home Printed from https://ideas.repec.org/a/vrs/offsta/v32y2016i1p187-208n9.html
   My bibliography  Save this article

Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model

Author

Listed:
  • Nandram Balgobin

    (Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, U.S.A.)

Abstract

We extend the twofold small-area model of Stukel and Rao (1997; 1999) to accommodate binary data. An example is the Third International Mathematics and Science Study (TIMSS), in which pass-fail data for mathematics of students from US schools (clusters) are available at the third grade by regions and communities (small areas). We compare the finite population proportions of these small areas. We present a hierarchical Bayesian model in which the firststage binary responses have independent Bernoulli distributions, and each subsequent stage is modeled using a beta distribution, which is parameterized by its mean and a correlation coefficient. This twofold small-area model has an intracluster correlation at the first stage and an intercluster correlation at the second stage. The final-stage mean and all correlations are assumed to be noninformative independent random variables. We show how to infer the finite population proportion of each area. We have applied our models to synthetic TIMSS data to show that the twofold model is preferred over a onefold small-area model that ignores the clustering within areas. We further compare these models using a simulation study, which shows that the intracluster correlation is particularly important.

Suggested Citation

  • Nandram Balgobin, 2016. "Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model," Journal of Official Statistics, Sciendo, vol. 32(1), pages 187-208, March.
  • Handle: RePEc:vrs:offsta:v:32:y:2016:i:1:p:187-208:n:9
    DOI: 10.1515/jos-2016-0009
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jos-2016-0009
    Download Restriction: no

    File URL: https://libkey.io/10.1515/jos-2016-0009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tomohiro Ando & Ruey S. Tsay, 2009. "Model selection for generalized linear models with factor‐augmented predictors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 207-235, May.
    2. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    3. Tomohiro Ando, 2012. "Bayesian portfolio selection under a multifactor asset return model with predictive model selection," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 14(1/2), pages 77-101.
    4. Ando, Tomohiro, 2009. "Bayesian inference for the hazard term structure with functional predictors using Bayesian predictive information criteria," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1925-1939, April.
    5. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
    6. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2015. "A Variant of AIC Using Bayesian Marginal Likelihood," CIRJE F-Series CIRJE-F-971, CIRJE, Faculty of Economics, University of Tokyo.
    7. Stefano Grassi & Francesco Ravazzolo & Joaquin Vespignani & Giorgio Vocalelli, 2023. "Global Money Supply and Energy and Non-Energy Commodity Prices: A MS-TV-VAR Approach," CAMA Working Papers 2023-13, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. Ando, Tomohiro, 2009. "Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1717-1726, September.
    9. Brady J Mattsson & Elise F Zipkin & Beth Gardner & Peter J Blank & John R Sauer & J Andrew Royle, 2013. "Explaining Local-Scale Species Distributions: Relative Contributions of Spatial Autocorrelation and Landscape Heterogeneity for an Avian Assemblage," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-12, February.
    10. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    11. Wang, Yixin & So, Mike K.P., 2016. "A Bayesian hierarchical model for spatial extremes with multiple durations," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 39-56.
    12. Filidor Vilca & Caio L. N. Azevedo & N. Balakrishnan, 2017. "Bayesian inference for sinh-normal/independent nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2052-2074, August.
    13. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2018. "A Variant of AIC Based on the Bayesian Marginal Likelihood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 60-84, May.
    14. Jincheol Park & Shili Lin, 2017. "A random effect model for reconstruction of spatial chromatin structure," Biometrics, The International Biometric Society, vol. 73(1), pages 52-62, March.
    15. Ando, Tomohiro, 2009. "Bayesian portfolio selection using a multifactor model," International Journal of Forecasting, Elsevier, vol. 25(3), pages 550-566, July.
    16. Michael T. Owyang & Hannah Shell & Daniel Soques, 2022. "The Evolution of Regional Beveridge Curves," Working Papers 2022-037, Federal Reserve Bank of St. Louis.
    17. Liang Yulan & Kelemen Arpad, 2016. "Bayesian state space models for dynamic genetic network construction across multiple tissues," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(4), pages 273-290, August.
    18. Cristina Mollica & Luca Tardella, 2017. "Bayesian Plackett–Luce Mixture Models for Partially Ranked Data," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 442-458, June.
    19. Toda, Motomu & Doi, Kazuki & Ishihara, Masae I. & Azuma, Wakana A. & Yokozawa, Masayuki, 2020. "A Bayesian inversion framework to evaluate parameter and predictive inference of a simple soil respiration model in a cool-temperate forest in western Japan," Ecological Modelling, Elsevier, vol. 418(C).
    20. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:offsta:v:32:y:2016:i:1:p:187-208:n:9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.sciendo.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.