IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v31y2022i1d10.1007_s11749-021-00776-w.html
   My bibliography  Save this article

A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates

Author

Listed:
  • Jan Pablo Burgard

    (Trier University)

  • Joscha Krause

    (Trier University)

  • Domingo Morales

    (University Miguel Hernández de Elche)

Abstract

The assessment of prevalence on regional levels is an important element of public health reporting. Since regional prevalence is rarely collected in registers, corresponding figures are often estimated via small area estimation using suitable health data. However, such data are frequently subject to uncertainty as values have been estimated from surveys. In that case, the method for prevalence estimation must explicitly account for data uncertainty to allow for reliable results. This can be achieved via measurement error models that introduce distribution assumptions on the noisy data. However, these methods usually require target and explanatory variable errors to be independent. This does not hold when data for both have been estimated from the same survey, which is sometimes the case in official statistics. If not accounted for, prevalence estimates can be severely biased. We propose a new measurement error model for regional prevalence estimation that is suitable for settings where target and explanatory variable errors are dependent. We derive empirical best predictors and demonstrate mean-squared error estimation. A maximum likelihood approach for model parameter estimation is presented. Simulation experiments are conducted to prove the effectiveness of the method. An application to regional hypertension prevalence estimation in Germany is provided.

Suggested Citation

  • Jan Pablo Burgard & Joscha Krause & Domingo Morales, 2022. "A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 204-234, March.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00776-w
    DOI: 10.1007/s11749-021-00776-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-021-00776-w
    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/s11749-021-00776-w?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. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    2. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    3. González-Manteiga, W. & Lombardi­a, M.J. & Molina, I. & Morales, D. & Santamari­a, L., 2008. "Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5242-5252, August.
    4. Marhuenda, Yolanda & Molina, Isabel & Morales, Domingo, 2013. "Small area estimation with spatio-temporal Fay–Herriot models," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 308-325.
    5. Azka Ubaidillah & Khairil Anwar Notodiputro & Anang Kurnia & I. Wayan Mangku, 2019. "Multivariate Fay-Herriot models for small area estimation with application to household consumption per capita expenditure in Indonesia," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(15), pages 2845-2861, November.
    6. Serena Arima & William R. Bell & Gauri S. Datta & Carolina Franco & Brunero Liseo, 2017. "Multivariate Fay–Herriot Bayesian estimation of small area means under functional measurement error," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1191-1209, October.
    7. Lynn M. R. Ybarra & Sharon L. Lohr, 2008. "Small area estimation when auxiliary information is measured with error," Biometrika, Biometrika Trust, vol. 95(4), pages 919-931.
    8. Alina Jędrzejczak & Jan Kubacki, 2017. "Estimation Of Small Area Characteristics Using Multivariate Rao-Yu Model," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 725-742, December.
    9. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    10. Esteban, M.D. & Morales, D. & Pérez, A. & Santamaría, L., 2012. "Small area estimation of poverty proportions under area-level time models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2840-2855.
    11. Mahmoud Torabi & Gauri S. Datta & J. N. K. Rao, 2009. "Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 355-369, June.
    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. Jan Pablo Burgard & Domingo Morales & Anna-Lena Wölwer, 2022. "Small area estimation of socioeconomic indicators for sampled and unsampled domains," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 287-314, June.
    2. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2021. "Small area estimation under a measurement error bivariate Fay–Herriot model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 79-108, March.
    3. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2020. "A Fay–Herriot model when auxiliary variables are measured with error," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 166-195, March.
    4. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2023. "Small area estimation of average compositions under multivariate nested error regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 651-676, June.
    5. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    6. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    7. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    8. Isabel Molina & Paul Corral & Minh Nguyen, 2022. "Estimation of poverty and inequality in small areas: review and discussion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1143-1166, December.
    9. Domingo Morales & Joscha Krause & Jan Pablo Burgard, 2022. "On the Use of Aggregate Survey Data for Estimating Regional Major Depressive Disorder Prevalence," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 344-368, March.
    10. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    11. 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.
    12. Shonosuke Sugasawa & Tatsuya Kubokawa & J. N. K. Rao, 2018. "Small area estimation via unmatched sampling and linking models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 407-427, June.
    13. María Dolores Esteban & María José Lombardía & Esther López‐Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Empirical best prediction of small area bivariate parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1699-1727, December.
    14. Priyanka Anjoy, 2023. "Hierarchical Bayes Measurement Error Small Area Model for Estimation of Disaggregated Level Workers Mobility Pattern in India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 339-361, June.
    15. J. N. K. Rao, 2015. "Inferential Issues In Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    16. Marhuenda, Yolanda & Morales, Domingo & del Carmen Pardo, María, 2014. "Information criteria for Fay–Herriot model selection," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 268-280.
    17. Szymkowiak Marcin & Młodak Andrzej & Wawrowski Łukasz, 2017. "Mapping Poverty at the Level of Subregions in Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.
    18. Marcin Szymkowiak & Andrzej Młodak & Łukasz Wawrowski, 2017. "Mapping Poverty At The Level Of Subregions In Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.
    19. Jan Kordos, 2016. "Development Of Smallarea Estimation In Official Statistics," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 105-132, March.
    20. repec:csb:stintr:v:17:y:2016:i:1:p:105-132 is not listed on IDEAS
    21. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.

    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:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00776-w. 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.