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Empirical best prediction under area-level Poisson mixed models

Author

Listed:
  • Miguel Boubeta

    (Universidade da Coruña)

  • María José Lombardía

    (Universidade da Coruña)

  • Domingo Morales

    (Universidad Miguel Hernández de Elche)

Abstract

The paper studies the applicability of area-level Poisson mixed models to estimate small area counting indicators. Among the available procedures for fitting generalized linear models, the method of moments (MM) and the penalised quasi-likelihood (PQL) method are employed. The empirical best predictor (EBP) of the area mean is derived using MM and compared with plug-in alternatives using MM and PQL. The plug-in estimator using PQL is computationally faster and provides competitive performance with respect to EBP that involves high complex integrals. An approximation to the mean squared error (MSE) of the EBP is given and three MSE estimators are proposed. The first two MSE estimators are plug-in estimators without and with bias correction to the second order and the third one is based on parametric bootstrap. Several simulation experiments are carried out for analysing the behaviour of the EBP and for comparing the estimators of the MSE of the EBP. A good choice in practice is the bootstrap alternative since it performs similarly to the analytical versions and is computationally faster. The developed methodology and software are applied to data from the 2008 Spanish living condition survey. The target of the application is the estimation of poverty rates at province level.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:3:d:10.1007_s11749-015-0469-8
    DOI: 10.1007/s11749-015-0469-8
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    References listed on IDEAS

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    1. 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.
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    4. Esther López-Vizcaíno & María José Lombardía & Domingo Morales, 2015. "Small area estimation of labour force indicators under a multinomial model with correlated time and area effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 535-565, June.
    5. J.N.K. Rao, 2008. "Some Methods for Small Area Estimation," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 116(4), pages 387-405.
    6. Soumendra N. Lahiri & Tapabrata Maiti & Myron Katzoff & Van Parsons, 2007. "Resampling-based empirical prediction: an application to small area estimation," Biometrika, Biometrika Trust, vol. 94(2), pages 469-485.
    7. MacNab, Ying C. & Lin, Yi, 2009. "On empirical Bayes penalized quasi-likelihood inference in GLMMs and in Bayesian disease mapping and ecological modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2950-2967, June.
    8. Jiming Jiang & P. Lahiri, 2001. "Empirical Best Prediction for Small Area Inference with Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 217-243, June.
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    Cited by:

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    2. 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.
    3. Flores-Agreda, Daniel & Cantoni, Eva, 2019. "Bootstrap estimation of uncertainty in prediction for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 1-17.
    4. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "$$\ell _2$$ ℓ 2 -penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 459-489, May.
    5. Adam Chwila & Tomasz Żądło, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 35-60, June.
    6. 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.
    7. 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.
    8. Jan Pablo Burgard & Joscha Krause & Ralf Münnich, 2019. "Penalized Small Area Models for the Combination of Unit- and Area-level Data," Research Papers in Economics 2019-05, University of Trier, Department of Economics.
    9. 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.
    10. 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.
    11. Chwila Adam & Żądło Tomasz, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Statistics Poland, vol. 21(2), pages 35-60, June.
    12. M. Giovanna Ranalli & Giorgio E. Montanari & Cecilia Vicarelli, 2018. "Estimation of small area counts with the benchmarking property," METRON, Springer;Sapienza Università di Roma, vol. 76(3), pages 349-378, December.
    13. 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.
    14. 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.
    15. Chandra, Hukum & Salvati, Nicola & Chambers, Ray, 2018. "Small area estimation under a spatially non-linear model," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 19-38.
    16. 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.

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