IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v29y2020i1d10.1007_s11749-019-00649-3.html
   My bibliography  Save this article

A Fay–Herriot model when auxiliary variables are measured with error

Author

Listed:
  • Jan Pablo Burgard

    (Trier University)

  • María Dolores Esteban

    (University Miguel Hernández de Elche)

  • Domingo Morales

    (University Miguel Hernández de Elche)

  • Agustín Pérez

    (University Miguel Hernández de Elche)

Abstract

The Fay–Herriot model is an area-level linear mixed model that is widely used for estimating the domain means of a given target variable. Under this model, the dependent variable is a direct estimator calculated by using the survey data and the auxiliary variables are true domain means obtained from external data sources. Administrative registers do not always give good auxiliary variables so that statisticians sometimes take them from alternative surveys and therefore they are measured with error. We introduce a variant of the Fay–Herriot model that takes into account the measurement error of the auxiliary variables and give two fitting algorithms that calculate maximum and residual maximum likelihood estimates of the model parameters. Based on the new model, empirical best predictors of domain means are introduced and an approximation of its mean squared error is derived. We finally give an application to estimate poverty proportions in the Spanish Living Condition Survey, with auxiliary information from the Spanish Labour Force Survey.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:1:d:10.1007_s11749-019-00649-3
    DOI: 10.1007/s11749-019-00649-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-019-00649-3
    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/s11749-019-00649-3?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. 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.
    2. 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.
    3. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    4. Serena Arima & Gauri S. Datta & Brunero Liseo, 2015. "Bayesian Estimators for Small Area Models when Auxiliary Information is Measured with Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 518-529, June.
    5. Malay Ghosh & Karabi Sinha & Dalho Kim, 2006. "Empirical and Hierarchical Bayesian Estimation in Finite Population Sampling under Structural Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 591-608, September.
    6. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    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. Tomáš Hobza & Domingo Morales & Laureano Santamaría, 2018. "Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed 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 270-294, June.
    9. 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.
    10. 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)

    Citations

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


    Cited by:

    1. Harm Jan Boonstra & Jan van den Brakel & Sumonkanti Das, 2021. "Multilevel time series modelling of mobility trends in the Netherlands for small domains," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 985-1007, July.
    2. Fúquene-Patiño Jairo & Cristancho César & Ospina Mariana & Gonzalez Domingo Morales, 2021. "Fay-Herriot Model-Based Prediction Alternatives for Estimating Households with Emigrated Members," Journal of Official Statistics, Sciendo, vol. 37(3), pages 771-789, September.

    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. 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.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. María Bugallo & Domingo Morales & María Dolores Esteban & Maria Chiara Pagliarella, 2024. "Model-Based Estimation of Small Area Dissimilarity Indexes: An Application to Sex Occupational Segregation in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 174(2), pages 473-501, September.
    10. Datta, Gauri S. & Torabi, Mahmoud & Rao, J.N.K. & Liu, Benmei, 2018. "Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 49-59.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Marchetti Stefano & Giusti Caterina & Pratesi Monica & Salvati Nicola & Giannotti Fosca & Pedreschi Dino & Rinzivillo Salvatore & Pappalardo Luca & Gabrielli Lorenzo, 2015. "Small Area Model-Based Estimators Using Big Data Sources," Journal of Official Statistics, Sciendo, vol. 31(2), pages 263-281, June.
    16. 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.
    17. Domingo Morales & María del Mar Rueda & Dolores Esteban, 2018. "Model-Assisted Estimation of Small Area Poverty Measures: An Application within the Valencia Region in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 873-900, August.
    18. Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    19. 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.
    20. Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.

    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:29:y:2020:i:1:d:10.1007_s11749-019-00649-3. 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.