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Small area estimates of labour force participation under a multinomial logit mixed model

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  • Isabel Molina
  • Ayoub Saei
  • M. José Lombardía

Abstract

Summary. A new methodology is developed for estimating unemployment or employment characteristics in small areas, based on the assumption that the sample totals of unemployed and employed individuals follow a multinomial logit model with random area effects. The method is illustrated with UK labour force data aggregated by sex–age groups. For these data, the accuracy of direct estimates is poor in comparison with estimates that are derived from the multinomial logit model. Furthermore, two different estimators of the mean‐squared errors are given: an analytical approximation obtained by Taylor linearization and an estimator based on bootstrapping. A simulation study for comparison of the two estimators shows the good performance of the bootstrap estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:170:y:2007:i:4:p:975-1000
    DOI: 10.1111/j.1467-985X.2007.00493.x
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    References listed on IDEAS

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    1. Gonzalez-Manteiga, W. & Lombardia, M.J. & Molina, I. & Morales, D. & Santamaria, L., 2007. "Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2720-2733, February.
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    4. 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.
    5. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    6. Danny Pfeffermann & Richard Tiller, 2005. "Bootstrap Approximation to Prediction MSE for State–Space Models with Estimated Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 893-916, November.
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    Cited by:

    1. 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.
    2. Alison Whitworth & Kirsten Piller & Angela Luna & Li-Chun Zhang, 2015. "Small area estimates of the population distribution by ethnic group in England: a proposal using structure preserving estimators," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 585-602, December.
    3. Angela Luna & Li-Chun Zhang & Alison Whitworth & Kirsten Piller, 2015. "Small Area Estimates Of The Population Distribution By Ethnic Group In England: A Proposal Using Structure Preserving Estimators," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 585-602, December.
    4. Isabel Molina & Ewa Strzalkowska‐Kominiak, 2020. "Estimation of proportions in small areas: application to the labour force using the Swiss Census Structural Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 281-310, January.
    5. Merfeld, Joshua D. & Newhouse, David & Weber, Michael & Lahiri, Partha, 2022. "Combining Survey and Geospatial Data Can Significantly Improve Gender-Disaggregated Estimates of Labor Market Outcomes," IZA Discussion Papers 15390, Institute of Labor Economics (IZA).
    6. 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.
    7. Luna Angela & Zhang Li-Chun & Whitworth Alison & Piller Kirsten, 2015. "Small Area Estimates of the Population Distribution by Ethnic Group in England: A Proposal Using Structure Preserving Estimators," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 585-602, December.
    8. Kawakubo, Yuki & Kobayashi, Genya, 2023. "Small area estimation of general finite-population parameters based on grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    9. J. L. Scealy & A. H. Welsh, 2017. "A Directional Mixed Effects Model for Compositional Expenditure Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 24-36, January.
    10. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.
    11. Alfredo A. Romero, 2014. "Where do Moderation Terms Come from in Binary Choice Models?," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(1), pages 57-68, March.
    12. 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.
    13. James Dawber & Nicola Salvati & Enrico Fabrizi & Nikos Tzavidis, 2022. "Expectile regression for multi‐category outcomes with application to small area estimation of labour force participation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 590-619, December.
    14. 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.
    15. 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.
    16. 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.
    17. Paul Walter & Marcus Groß & Timo Schmid & Nikos Tzavidis, 2021. "Domain prediction with grouped income data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1501-1523, October.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. Fabrizi, Enrico & Ferrante, Maria Rosaria & Pacei, Silvia & Trivisano, Carlo, 2011. "Hierarchical Bayes multivariate estimation of poverty rates based on increasing thresholds for small domains," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1736-1747, April.
    23. 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.

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