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Multivariate Fay–Herriot Bayesian estimation of small area means under functional measurement error

Author

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  • Serena Arima
  • William R. Bell
  • Gauri S. Datta
  • Carolina Franco
  • Brunero Liseo

Abstract

Area level models, such as the Fay–Herriot model, aim to improve direct survey estimates for small areas by borrowing strength from related covariates and from direct estimates across all areas. In their multivariate form, where related population characteristics are jointly modelled, area level models allow for inference about functions of two or more characteristics and may exploit dependence between the response variables to improve small area predictions. When model covariates are observed with random error, such as those drawn from another survey, it is important to account for this error in the modelling. We present a Bayesian analysis of a multivariate Fay–Herriot model with functional measurement error, allowing for both joint modelling of related characteristics and accounting for random observation error in some of the covariates. We apply it to modelling 2010 and 2011 poverty rates of school‐aged children for US counties, for predicting 2011 poverty rates and the 2010–2011 changes. For this application, the measurement error model results in great improvements in prediction when compared with the direct estimates, and ignoring the measurement error results in uncertainty estimates that are misleading. We propose a computational approach to implementing this model via an independence chain Markov chain Monte Carlo algorithm and prove the propriety of the posterior distribution under a class of non‐informative priors.

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  • 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.
    • Handle: RePEc:bla:jorssa:v:180:y:2017:i:4:p:1191-1209
    DOI: 10.1111/rssa.12321
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    References listed on IDEAS

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    1. Russell D. Wolfinger & Robert E. Kass, 2000. "Nonconjugate Bayesian Analysis of Variance Component Models," Biometrics, The International Biometric Society, vol. 56(3), pages 768-774, September.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. 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.
    2. Bijlsma Ineke & van den Brakel Jan & van der Velden Rolf & Allen Jim, 2020. "Estimating Literacy Levels at a Detailed Regional Level: an Application Using Dutch Data," Journal of Official Statistics, Sciendo, vol. 36(2), pages 251-274, June.
    3. Caio Gonçalves & Luna Hidalgo & Denise Silva & Jan van den Brakel, 2022. "Single‐month unemployment rate estimates for the Brazilian Labour Force Survey using state‐space models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1707-1732, October.
    4. 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.
    5. 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.
    6. Charles R. Collins & Forrest Stuart & Patrick Janulis, 2022. "Policing gentrification or policing displacement? Testing the relationship between order maintenance policing and neighbourhood change in Los Angeles," Urban Studies, Urban Studies Journal Limited, vol. 59(2), pages 414-433, February.
    7. 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.
    8. 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.
    9. 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.
    10. van den Brakel Jan & Michiels John, 2021. "Nowcasting Register Labour Force Participation Rates in Municipal Districts Using Survey Data," Journal of Official Statistics, Sciendo, vol. 37(4), pages 1009-1045, December.
    11. 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.
    12. 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.
    13. 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.

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