IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v23y2018i4d10.1007_s13253-018-0329-6.html
   My bibliography  Save this article

Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey

Author

Listed:
  • Xin Wang

    (Miami University)

  • Emily Berg

    (Iowa State University)

  • Zhengyuan Zhu

    (Iowa State University)

  • Dongchu Sun

    (University of Missouri-Columbia
    East China Normal University)

  • Gabriel Demuth

    (Iowa State University)

Abstract

Motivated by the need to produce small area estimates for the National Resources Inventory survey, we develop a spatial hierarchical model based on the generalized Dirichlet distribution to construct small area estimators of compositional proportions in several mutually exclusive and exhaustive landcover categories. At the observation level, the standard design-based estimators of the proportions are assumed to follow the generalized Dirichlet distribution. After proper transformation of the design-based estimators, beta regression is applicable. We consider a logit mixed model for the expectation of the beta distribution, which incorporates covariates through fixed effects and spatial effect through a conditionally autoregressive process. In a design-based evaluation study, the proposed model-based estimators are shown to have smaller root-mean-square error and relative root-mean-square error than design-based estimators and multinomial model-based estimators. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Xin Wang & Emily Berg & Zhengyuan Zhu & Dongchu Sun & Gabriel Demuth, 2018. "Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 509-528, December.
    • Handle: RePEc:spr:jagbes:v:23:y:2018:i:4:d:10.1007_s13253-018-0329-6
    DOI: 10.1007/s13253-018-0329-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-018-0329-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-018-0329-6?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tapabrata Maiti & Hao Ren & Samiran Sinha, 2014. "Prediction Error of Small Area Predictors Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 775-790, September.
    2. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    3. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    5. Alan Agresti & David B. Hitchcock, 2005. "Bayesian inference for categorical data analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 297-330, December.
    6. Chongyang Jin & Jun Zhu & Michelle M. Steen‐Adams & Stephan R. Sain & Ronald E. Gangnon, 2013. "Spatial multinomial regression models for nominal categorical data: a study of land cover in Northern Wisconsin, USA," Environmetrics, John Wiley & Sons, Ltd., vol. 24(2), pages 98-108, March.
    7. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
    8. Jiang, Jiming & Lahiri, P., 2006. "Estimation of Finite Population Domain Means: A Model-Assisted Empirical Best Prediction Approach," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 301-311, March.
    9. Zhuoqiong He & Dongchu Sun, 2000. "Hierarchical Bayes Estimation of Hunting Success Rates with Spatial Correlations," Biometrics, The International Biometric Society, vol. 56(2), pages 360-367, June.
    10. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Xin & Zhu, Zhengyuan & Zhang, Hao Helen, 2023. "Spatial heterogeneity automatic detection and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    2. Hao Sun & Emily Berg & Zhengyuan Zhu, 2022. "Bivariate small‐area estimation for binary and gaussian variables based on a conditionally specified model," Biometrics, The International Biometric Society, vol. 78(4), pages 1555-1565, December.

    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. Edilberto Cepeda-Cuervo & Vicente Núñez-Antón, 2013. "Spatial Double Generalized Beta Regression Models," Journal of Educational and Behavioral Statistics, , vol. 38(6), pages 604-628, December.
    2. Cepeda-Cuervo Edilberto & Garrido Liliana, 2015. "Bayesian beta regression models with joint mean and dispersion modeling," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 49-58, March.
    3. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    4. Grün, Bettina & Kosmidis, Ioannis & Zeileis, Achim, 2012. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i11).
    5. Dries P.J. Kuijper & Jakub W. Bubnicki & Marcin Churski & Bjorn Mols & Pim van Hooft, 2015. "Context dependence of risk effects: wolves and tree logs create patches of fear in an old-growth forest," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(6), pages 1558-1568.
    6. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    7. Maria Gheorghe & Susan Picavet & Monique Verschuren & Werner B. F. Brouwer & Pieter H. M. Baal, 2017. "Health losses at the end of life: a Bayesian mixed beta regression approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(3), pages 723-749, June.
    8. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    9. Li-Chu Chien, 2013. "Multiple deletion diagnostics in beta regression models," Computational Statistics, Springer, vol. 28(4), pages 1639-1661, August.
    10. Min-Je Choi & Do-Hoon Kim, 2020. "Assessment and Management of Small Yellow Croaker ( Larimichthys polyactis ) Stocks in South Korea," Sustainability, MDPI, vol. 12(19), pages 1-17, October.
    11. Chibuzor Christopher Nnanatu & Glory Atilola & Paul Komba & Lubanzadio Mavatikua & Zhuzhi Moore & Dennis Matanda & Otibho Obianwu & Ngianga-Bakwin Kandala, 2021. "Evaluating changes in the prevalence of female genital mutilation/cutting among 0-14 years old girls in Nigeria using data from multiple surveys: A novel Bayesian hierarchical spatio-temporal model," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-31, February.
    12. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.
    13. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    14. Kaan Kuzu & Refik Soyer, 2018. "Bayesian modeling of abandonments in ticket queues," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 499-521, September.
    15. Yury R. Benites & Vicente G. Cancho & Edwin M. M. Ortega & Roberto Vila & Gauss M. Cordeiro, 2022. "A New Regression Model on the Unit Interval: Properties, Estimation, and Application," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    16. Giovanna Bua & Carmine Trecroci, 2019. "International equity markets interdependence: bigger shocks or contagion in the 21st century?," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 155(1), pages 43-69, February.
    17. Francisco Cribari-Neto & Sadraque E.F. Lucena, 2015. "Nonnested hypothesis testing in the class of varying dispersion beta regressions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 967-985, May.
    18. S. Upadhyay & M. Peshwani, 2008. "Posterior analysis of lognormal regression models using the Gibbs sampler," Statistical Papers, Springer, vol. 49(1), pages 59-85, March.
    19. Ngianga-Bakwin Kandala & Chibuzor Christopher Nnanatu & Glory Atilola & Paul Komba & Lubanzadio Mavatikua & Zhuzhi Moore & Gerry Mackie & Bettina Shell-Duncan, 2019. "A Spatial Analysis of the Prevalence of Female Genital Mutilation/Cutting among 0–14-Year-Old Girls in Kenya," IJERPH, MDPI, vol. 16(21), pages 1-28, October.
    20. Frank A. La Sorte & Alison Johnston & Toby R. Ault, 2021. "Global trends in the frequency and duration of temperature extremes," Climatic Change, Springer, vol. 166(1), pages 1-14, May.

    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:spr:jagbes:v:23:y:2018:i:4:d:10.1007_s13253-018-0329-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.