Advertisement

TEST

pp 1–26 | Cite as

Small area estimation of proportions under area-level compositional mixed models

  • María Dolores Esteban
  • María José Lombardía
  • Esther López-Vizcaíno
  • Domingo Morales
  • Agustín PérezEmail author
Original Paper
  • 50 Downloads

Abstract

This paper introduces area-level compositional mixed models by applying transformations to a multivariate Fay–Herriot model. Small area estimators of the proportions of the categories of a classification variable are derived from the new model, and the corresponding mean squared errors are estimated by parametric bootstrap. Several simulation experiments designed to analyse the behaviour of the introduced estimators are carried out. An application to real data from the Spanish Labour Force Survey of Galicia (north-west of Spain), in the first quarter of 2017, is given. The target is the estimation of domain proportions of people in the four categories of the variable labour status: under 16 years, employed, unemployed and inactive.

Keywords

Labour Force Survey Small area estimation Area-level models Compositional data Bootstrap Labour status 

Mathematics Subject Classification

62E30 62J12 

Notes

Supplementary material

11749_2019_688_MOESM1_ESM.pdf (300 kb)
Supplementary material 1 (pdf 299 KB)

References

  1. Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall, LondonzbMATHCrossRefGoogle Scholar
  2. Arima S, Bell WR, Datta GS, Franco C, Liseo B (2017) Multivariate Fay–Herriot Bayesian estimation of small area means under functional measurement error. J R Stat Soc Ser A 180(4):1191–1209MathSciNetCrossRefGoogle Scholar
  3. Benavent R, Morales D (2016) Multivariate Fay–Herriot models for small area estimation. Comput Stat Data Anal 94:372–390MathSciNetzbMATHCrossRefGoogle Scholar
  4. Berg E, Fuller WA (2012) Estimators of error covariance matrices for small area prediction. Comput Stat Data Anal 56:2949–2962MathSciNetzbMATHCrossRefGoogle Scholar
  5. Berg EJ, Fuller WA (2014) Small area prediction of proportions with applications to the Canadian Labour Force Survey. J Surv Stat Methodol 2:227–256CrossRefGoogle Scholar
  6. Boubeta M, Lombardía MJ, Morales D (2016) Empirical best prediction under area-level Poisson mixed models. TEST 25:548–569MathSciNetzbMATHCrossRefGoogle Scholar
  7. Boubeta M, Lombardía MJ, Morales D (2017) Poisson mixed models for studying the poverty in small areas. Comput Stat Data Anal 107:32–47MathSciNetzbMATHCrossRefGoogle Scholar
  8. Chambers R, Dreassi E, Salvati N (2014) Disease mapping via negative binomial regression M-quantiles. Stat Med 33:4805–4824MathSciNetCrossRefGoogle Scholar
  9. Chambers R, Salvati N, Tzavidis N (2016) Semiparametric small area estimation for binary outcomes with application to unemployment estimation for Local Authorities in the UK. J R Stat Soc Ser A 179:453–479MathSciNetCrossRefGoogle Scholar
  10. Chen S, Lahiri P (2012) Inferences on small area proportions. J Indian Soc Agric Stat 66(1):121–124MathSciNetGoogle Scholar
  11. Datta GS, Fay RE Ghosh M (1991) Hierarchical and empirical Bayes multivariate analysis in small area estimation. In: Proceedings of Bureau of the census 1991 annual research conference, U. S. Bureau of the Census, Washington, DC, pp 63–79Google Scholar
  12. Datta GS, Ghosh M, Nangia N, Natarajan K (1996) Estimation of median income of four-person families: a Bayesian approach. In: Berry DA, Chaloner KM, Geweke JM (eds) Bayesian analysis in statistics and econometrics. Wiley, New York, pp 129–140Google Scholar
  13. Dreassi E, Ranalli MG, Salvati N (2014) Semiparametric M-quantile regression for count data. Stat Methods Med Res 23:591–610MathSciNetCrossRefGoogle Scholar
  14. Egozcue JJ, Pawlowsky-Glahn V (2019) Compositional data: the sample space and its structure. TEST 28(3):599–638MathSciNetzbMATHCrossRefGoogle Scholar
  15. Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G, Barceló-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35(3):279–300MathSciNetzbMATHCrossRefGoogle Scholar
  16. Esteban MD, Morales D, Pérez A, Santamaría L (2012) Small area estimation of poverty proportions under area-level time models. Comput Stat Data Anal 56:2840–2855MathSciNetzbMATHCrossRefGoogle Scholar
  17. Fabrizi E, Ferrante MR, Trivisano C (2016) Hierarchical Beta regression models for the estimation of poverty and inequality parameters in small areas. In: Pratesi Monica (ed) Analysis of poverty data by small area methods. Wiley, New YorkzbMATHGoogle Scholar
  18. Farrell PJ (2000) Bayesian inference for small area estimation. Sankhya Ser B 62(3):402–416MathSciNetzbMATHGoogle Scholar
  19. Fay RE (1987) Application of multivariate regression of small domain estimation. In: Platek R, Rao JNK, Särndal CE, Singh MP (eds) Small area statistics. Wiley, New York, pp 91–102Google Scholar
  20. Ferrante MR, Trivisano C (2010) Small area estimation of the number of firms’ recruits by using multivariate models for count data. Surv Methodol 36(2):171–180Google Scholar
  21. Ghosh M, Nangia N, Kim D (1996) Estimation of median income of four-person families: a Bayesian time series approach. J Am Stat Assoc 91:1423–1431MathSciNetzbMATHCrossRefGoogle Scholar
  22. González-Manteiga W, Lombardía MJ, Molina I, Morales D, Santamaría L (2007) Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model. Comput Stat Data Anal 51:2720–33MathSciNetzbMATHCrossRefGoogle Scholar
  23. González-Manteiga W, Lombardía MJ, Molina I, Morales D, Santamaría L (2008a) Analytic and bootstrap approximations of prediction errors under a multivariate Fay–Herriot model. Comput Stat Data Anal 52:5242–5252MathSciNetzbMATHCrossRefGoogle Scholar
  24. González-Manteiga W, Lombardía MJ, Molina I, Morales D, Santamaría L (2008b) Bootstrap mean squared error of small-area EBLUP. J Stat Comput Simul 78:443–462MathSciNetzbMATHCrossRefGoogle Scholar
  25. Hobza T, Morales D (2016) Empirical best prediction under unit-level logit mixed models. J Off Stat 32(3):661–669CrossRefGoogle Scholar
  26. Hobza T, Santamaría L, Morales D (2018) Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models. TEST 27(2):270–294MathSciNetzbMATHCrossRefGoogle Scholar
  27. Larsen MD (2003) Estimation of small-area proportions using covariates and survey data. J Stat Plan Inference 112:89–98MathSciNetzbMATHCrossRefGoogle Scholar
  28. Liu B, Lahiri P (2017) Adaptive Hierarchical Bayes estimation of small area proportions. Calcutta Stat Assoc Bull 69(2):150–164MathSciNetCrossRefGoogle Scholar
  29. López-Vizcaíno E, Lombardía MJ, Morales D (2013) Multinomial-based small area estimation of labour force indicators. Stat Model 13(2):153–178MathSciNetCrossRefGoogle Scholar
  30. López-Vizcaíno E, Lombardía MJ, Morales D (2015) Small area estimation of labour force indicators under a multinomial model with correlated time and area effects. J R Stat Soc Ser A 178(3):535–565MathSciNetCrossRefGoogle Scholar
  31. Marhuenda Y, Molina I, Morales D (2013) Small area estimation with spatio-temporal Fay–Herriot models. Comput Stat Data Anal 58:308–325MathSciNetzbMATHCrossRefGoogle Scholar
  32. Marhuenda Y, Morales D, Pardo MC (2014) Information criteria for Fay–Herriot model selection. Comput Stat Data Anal 70:268–280MathSciNetzbMATHCrossRefGoogle Scholar
  33. Molina I, Saei A, Lombardía MJ (2007) Small area estimates of labour force participation under multinomial logit mixed model. J R Stati Soc Ser A 170:975–1000MathSciNetCrossRefGoogle Scholar
  34. Morales D, Pagliarella MC, Salvatore R (2015) Small area estimation of poverty indicators under partitioned area-level time models. SORT Stat Oper Res Trans 39(1):19–34MathSciNetzbMATHGoogle Scholar
  35. Pawlowsky-Glahn V, Buccianti A (eds) (2011) Compositional data analysis. Wiley, ChichesterzbMATHGoogle Scholar
  36. Rao JNK (2003) Small area estimation. Wiley, New-YorkzbMATHCrossRefGoogle Scholar
  37. Rao JNK, Molina I (2015) Small area estimation, 2nd edn. Wiley, HobokenzbMATHCrossRefGoogle Scholar
  38. Saei A, Chambers R (2003) Small area estimation under linear an generalized linear mixed models with time and area effects. S3RI Methodology Working Paper M03/15, Southampton Statistical Sciences Research InstituteGoogle Scholar
  39. Särndal CE, Swensson B, Wretman J (1992) Model assisted survey sampling. Springer, BerlinzbMATHCrossRefGoogle Scholar
  40. Scealy JL, Welsh AH (2017) A directional mixed effects model for compositional expenditure data. J Am Stat Assoc 112(517):24–36MathSciNetCrossRefGoogle Scholar
  41. Slud EV, Maiti T (2006) Mean-squared error estimation in transformed Fay–Herriot models. J R Stat Soc Ser B 68(2):239–257MathSciNetzbMATHCrossRefGoogle Scholar
  42. Souza DB, Moura FAS (2016) Multivariate Beta regression with applications in small area estimation. J Off Stat 32:747–768CrossRefGoogle Scholar
  43. Tzavidis N, Ranalli MG, Salvati N, Dreassi E, Chambers R (2015) Robust small area prediction for counts. Stat Methods Med Res 24(3):373–395MathSciNetCrossRefGoogle Scholar
  44. Zhang L, Chambers R (2004) Small area estimates for cross-classifications. J R Stat Soc Ser B 66(2):479–496MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Universidad Miguel Hernández de ElcheAlicanteSpain
  2. 2.CITICUniversidade da CoruñaA CoruñaSpain
  3. 3.Instituto Galego de EstatísticaSantiago de CompostelaSpain

Personalised recommendations