Small area estimation of additive parameters under unit-level generalized linear mixed models

  1. Tomáš Hobza 1
  2. Yolanda Marhuenda 2
  3. Domingo Morales 2
  1. 1 Czech Technical University in Prague
    info

    Czech Technical University in Prague

    Praga, República Checa

    ROR https://ror.org/03kqpb082

  2. 2 Universidad Miguel Hernández de Elche
    info

    Universidad Miguel Hernández de Elche

    Elche, España

    ROR https://ror.org/01azzms13

Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Año de publicación: 2020

Volumen: 44

Número: 1

Páginas: 3-38

Tipo: Artículo

DOI: 10.2436/20.8080.02.93 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Sort: Statistics and Operations Research Transactions

Resumen

Average incomes and poverty proportions are additive parameters obtained as averages of a given function of an income variable. As the variable income has an asymmetric distribution, it is not properly modelled via normal distributions. When dealing with this type of variable, a first option is to apply transformations that approximate normality. A second option is to use nonsymmetric distributions from the exponential family. This paper proposes unit-level generalized linear mixed models for modelling asymmetric positive variables and for deriving three types of predictors of small area additive parameters, called empirical best, marginal and plug-in. The parameters of the introduced model are estimated by applying the maximum likelihood method to the Laplace approximation of the likelihood. The mean squared errors of the predictors are estimated by parametric bootstrap. The introduced methodology is applied and illustrated under unit-level gamma mixed models. Some simulation experiments are carried out to study the behaviour of the fitting algorithm, the small area predictors and the bootstrap estimator of the mean squared errors. By using data of the Spanish living condition survey of 2013, an application to the estimation of average incomes and poverty proportions in counties of the region of Valencia is given.

€ Ver financiación

Información de financiación

This work was supported by the Spanish grant ePGC2018-096840-B-I00 from Ministerio de Econom?a y Competitividad, the Czech grant SGS18/188/OHK4/3T/14 provided by Ministry of Education, Youth and Sports (MSMT CR) and from European Regional Development Fund-Project "Center of Advanced Applied Sciences" (No. CZ.02.1.01/0.0/0.0/16-019/0000778).

Financiadores

Referencias bibliográficas

  • Benavent, R. and Morales, D. (2016). Multivariate Fay-Herriot models for small area estimation. Computational Statistics and Data Analysis, 94, 372-390.
  • Boubeta, M., Lombardı́a, M.J. and Morales, D. (2016). Empirical best prediction under area-level Poisson mixed models. TEST, 25, 548-569.
  • Boubeta, M., Lombardı́a, M.J. and Morales, D. (2017). Poisson mixed models for studying the poverty in small areas. Computational Statistics and Data Analysis, 107, 32-47.
  • Chambers, R., Salvati, N. and Tzavidis, N. (2012).M-Quantile Regression for Binary Data with Application to Small Area Estimation. Centre for Statistical and Survey Methodology, University of Wollongong. (Working Paper 12-12, 2012, 24). Available at: http://ro.uow.edu.au/cssmwp/101.
  • Chambers, R., Salvati, N. and Tzavidis, N. (2016). Semiparametric small area estimation for binary outcomes with application to unemployment estimation for local authorities in the UK. Journal of the Royal Statistical Society, Series A, 179, 2, 453-479.
  • Dreassi, E., Petrucci, A. and Rocco, E. (2014). Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany. Biometrical Journal, 56, 1, 141-156
  • Elbers, C., Lanjouw, J.O. and Lanjouw, P. (2003). Micro-level estimation of poverty and inequality. Econometrica, 71, 355-364.
  • Esteban, M.D., Morales, D., Pérez, A. and Santamarı́a, L. (2012a). Two Area-Level Time Models for Estimating Small Area Poverty Indicators. Journal of the Indian Society of Agricultural Statistics, 66, 1, 75-89.
  • Esteban, M.D., Morales, D., Pérez, A. and Santamarı́a, L. (2012b). Small area estimation of poverty proportions under area-level time models. Computational Statistics and Data Analysis, 56, 2840-2855.
  • Fabrizi, E., Ferrante, M.R. and Trivisano, C. (2017). Bayesian small area estimation for skewed business survey variables. Jornal of the Royal Statistical Society, Series C. doi.org/10.1111/rssc.12254
  • González-Manteiga, W., Lombardı́a, M.J., Molina, I., Morales, D. and Santamarı́a, L. (2007). Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model. Computational Statistics and Data Analysis, 51, 2720-2733.
  • González-Manteiga, W., Lombardı́a, M.J., Molina, I., Morales, D. and Santamarı́a, L. (2008a). Bootstrap mean squared error of small-area EBLUP. Journal of Statistical Computation and Simulation, 78, 443- 462.
  • González-Manteiga, W., Lombardı́a, M.J., Molina, I., Morales, D. and Santamarı́a, L. (2008b). Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model. Computational Statistics and Data Analysis, 52, 5242-5252.
  • Guadarrama, M., Molina, I. and Rao, J.N.K. (2014). A comparison of small area estimation methods for poverty mapping. Statistics in Transition new series and Survey Methodology, 17, 41-66.
  • Hall, P. and Maiti, T. (2006a). Nonparametric estimation of mean-squared prediction error in nested-error regression models. Annals of Statistics, 34, 4, 1733-1750.
  • Hall, P. and Maiti, T. (2006b). On parametric bootstrap methods for small-area prediction. Journal of the Royal Statistical Society, B, 68, 221-238.
  • Hobza, T. and Morales, D. (2013). Small area estimation under random regression coefficient models. Journal of Statistical Computation and Simulation, 83, 11, 2160-2177.
  • Hobza, T. and Morales, D. (2016). Empirical Best Prediction Under Unit-Level Logit Mixed Models. Journal of official statistics, 32, 3, 661-692.
  • Hobza, T., Morales, D. and Santamarı́a, L. (2018). Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models. TEST, 27, N. 2., 270-294.
  • Karlberg, F. (2014). Small area estimation for skewed data in the presence of zeroes. Statistics in Transition, 16, 4, 541-562.
  • Marhuenda, Y., Molina, I. and Morales, D. (2013). Small area estimation with spatio-temporal Fay-Herriot models. Computational Statistics and Data Analysis, 58, 308-325.
  • Marhuenda, Y., Molina, I., Morales, D. and Rao, J.N.K. (2017). Poverty mapping in small areas under a two-fold nested error regression model. Journal of the Royal Statistical Society, series A, 180, 4, 1111- 1136.
  • Molina, I., Nandram, B. and Rao, J.N.K. (2015). Small area estimation of general parameters with application to poverty indicators: a hierarchical Bayes approach. The Annals of Applied Statistics, 8, 852-885.
  • Molina, I. and Rao, J.N.K. (2010). Small area estimation of poverty indicators. The Canadian Journal of Statistics, 38, 369-385.
  • Morales, D., Pagliarella, M.C. and Salvatore, R. (2015). Small area estimation of poverty indicators under partitioned area-level time models. SORT-Statistics and Operations Research Transactions, 39, 1, 19-34.
  • Moura, F.A.S., Silva, D. B. N. and Neves, A.F. (2017). Small area models for skewed Brazilian business survey data. Jornal of the Royal Statistical Society, Series A, 180, 4, 1039-1055.
  • Pratesi, M. (2016). Analysis of Poverty Data by Small Area Estimation. John Wiley.
  • R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
  • Rao J. N. K. and Molina, I. (2015). Small Area Estimation, 2nd Edition, New York: Wiley.
  • Sinha, S.K. and Rao, J.N.K. (2009). Robust small area estimation. The Canadian Journal of Statistics, 37, 381-399.
  • Tzavidis, N., Salvati, N., Pratesi, M. and Chambers, R. (2008). M-quantile models with application to poverty mapping. Statistical Methods and Applications, 17, 3, 393-411. https://www.R-project.org/
Fuente de los datos: Dialnet