Published

2016-07-01

The Performance of Multivariate Calibration on Ratios, Means and Proportions

Sobre la calibración multivariada sobre razones, medias y proporciones

DOI:

https://doi.org/10.15446/rce.v39n2.55424

Keywords:

Calibration, Survey sampling, Ratio estimation, Nonlinear estimation, Monte Carlo simulation (en)
Calibración, Encuestas por muestreo, Estimación de razón, Estimadores no lineales, Simulación Monte Carlo. (es)

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Authors

  • Hugo Andrés Gutiérrez Universidad Santo Tomás
  • Hanwen Zhang Universidad Santo Tomás
  • Nelson Andrés Rodríguez Instituto Colombiano para la Evaluación de la Educación (ICFES)

In this paper, the calibration approach is revisited in order to allow new
calibration weights that are subject to the restriction of multiple calibration equations on a vector of ratios, means and proportions. The classical approach is extended in such a way that the calibration equations are not based on a vector of totals, but on a vector of other nonlinear parameters. We stated some properties of the resulting estimators and carry out some empirical simulations in order to asses the performance of this approach. We found that this methodology is suitable for some practical situations like vote intention estimation, estimation of labor force, and retrospective studies. The methodology is applied in the context of the Presidential elections held in Colombia in 2014 for which we estimated the vote intention in the second round using information from an election poll, taking the results from
the first round as auxiliary information.

En este artículo se aborda la metodología de calibración que reproduce pesos nuevos sujeto la restricción de las ecuaciones de calibración múltiple sobre un vector de razones, medias o proporciones. Se extiende la calibración clásica de tal forma que las ecuaciones de calibración no estén basados solo un vector de totales, sino un vector de parámetros no lineales. Se dan algunas propiedades de los estimadores resultantes y se llevan a cabo algunas simulaciones empíricas para verificar el desempeño de este enfoque. Encontramos que este es apropiado para algunas situaciones prácticas tales como la estimación de la intención de voto, estimación de fuerza laboral y estudios retrospectivos. La metodología es aplicada en el contexto de las elecciones presidenciales de Colombia en el 2014, donde estimamos la intención de voto en la segunda vuelta utilizando datos provenientes de una encuesta electoral tomando los resultados de la primera vuelta como información auxiliar.

https://doi.org/10.15446/rce.v39n2.55424

The Performance of Multivariate Calibration on Ratios, Means and Proportions

Sobre la calibración multivariada sobre razones, medias y proporciones

HUGO ANDRÉS GUTIÉRREZ ROJAS1, HANWEN ZHANG2, NELSON ANDRÉS RODRÍGUEZ3

1Universidad Santo Tomás, División de Ciencias Económicas y Administrativas, Facultad de Estadística, Bogotá, Colombia. Professor. Email: hugogutierrez@usantotomas.edu.co
2Universidad Santo Tomás, División de Ciencias Económicas y Administrativas, Facultad de Estadística, Bogotá, Colombia. Professor. Email: hanwenzhang@usantotomas.edu.co
3Instituto Colombiano para la Evaluación de la Educación (ICFES), Bogotá, Colombia. Statistic. Email: nrodriguez@icfes.gov.co

Abstract

In this paper, the calibration approach is revisited in order to allow new calibration weights that are subject to the restriction of multiple calibration equations on a vector of ratios, means and proportions. The classical approach is extended in such a way that the calibration equations are not based on a vector of totals, but on a vector of other nonlinear parameters. We stated some properties of the resulting estimators and carry out some empirical simulations in order to asses the performance of this approach. We found that this methodology is suitable for some practical situations like vote intention estimation, estimation of labor force, and retrospective studies. The methodology is applied in the context of the Presidential elections held in Colombia in 2014 for which we estimated the vote intention in the second round using information from an election poll, taking the results from the first round as auxiliary information.

Key words: Calibration, Survey sampling, Ratio estimation, Nonlinear estimation, Monte Carlo simulation.

Resumen

En este artículo se aborda la metodología de calibración que reproduce pesos nuevos sujeto la restricción de las ecuaciones de calibración múltiple sobre un vector de razones, medias o proporciones. Se extiende la calibración clásica de tal forma que las ecuaciones de calibración no estén basados solo un vector de totales, sino un vector de parámetros no lineales. Se dan algunas propiedades de los estimadores resultantes y se llevan a cabo algunas simulaciones empíricas para verificar el desempeño de este enfoque. Encontramos que este es apropiado para algunas situaciones prácticas tales como la estimación de la intención de voto, estimación de fuerza laboral y estudios retrospectivos. La metodología es aplicada en el contexto de las elecciones presidenciales de Colombia en el 2014, donde estimamos la intención de voto en la segunda vuelta utilizando datos provenientes de una encuesta electoral tomando los resultados de la primera vuelta como información auxiliar.

Palabras clave: calibración, encuestas por muestreo, estimación de razón, estimadores no lineales, simulación Monte Carlo.

Texto completo disponible en PDF

References

1. Blais, A., Massicotte, L. & Dobrzynska, A. (1997), 'Direct presidential elections: a world summary', Electoral Studies 16(4), 441-455.

2. Bouton, L. & Gratton, G. (2015), 'Majority runoff elections: strategic voting and duverger's hypothesis', Theoretical Economics 10, 283-314.

3. Brewer, K. R. W. (1999), 'Cosmetic calibration with unequal probability sampling', Survey Methodology 25(2), 205-212.

4. Deville, Jean-Claude & Sarndal, Carl-Erik (1992), 'Calibration estimators in survey sampling', Journal of the American statistical Association 87(418), 376-382.

5. Estevao, V. M. & Sarndal, C-E. (2006), 'Survey estimates by calibration on complex auxiliary information', International Statistical Review 74(2), 127-147.

6. Estevao, V. M., Sarndal, C-E. & Sautory, O. (2000), 'A functional form approach to calibration', Journal of Official Statistics 16, 379-399.

7. Estevao, V. M. & Sarndal, C. E. (2004), 'Borrowing Strength Is Not the Best Technique Within a Wide Class of Design-Consistent Domain Estimators', Journal of Official Statistics 20(4), 645-669.

8. Kim, J. K. & Park, M. (2010), 'Calibration estimation in survey sampling', International Statistical Review 78(1), 21-39.

9. Kim, Jong-Min, Sungur, E. A. & Heo, Tae-Young (2007), 'Calibration approach estimators in stratified sampling', Statistics & Probability Letters 77(1), 99-103.

10. Kott, P. S. (2003), 'A practical use for instrumental-variable calibration', Journal of Official Statistics 19(3), 265-272.

11. Kott, P. S. (2004), 'Comment on Demnati and Rao: Linarization variance estimators for survey data', Survey Methodology 30, 27-28.

12. Krapavickaite, D. & Plikusas, A. (2005), 'Estimation of a ratio in the finite population', Informatica 16(3), 347-364.

13. Lesage, E. (2011), 'The use of estimating equations to perform a calibration on complex parameters', Survey methodology 37(1), 103-108.

14. Park, S. & Kim, J. K. (2014), 'Instrumental-variable calibration estimation in survey sampling', Statistica Sinica 24, 1001-1015.

15. Perez-Liñan, A. (2006), 'Evaluating presidential runoff elections', Electoral Studies 25(1), 129-146.

16. Plikusas, A. (2006), Non-linear calibration, 'Proceedings, Workshop on survey sampling', Venspils, Latvia. Riga: Central Statistical Bureau of Latvia..

17. R Development Core Team, (2007), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *http://www.R-project.org

18. Sarndal, C. E. (2007), 'The calibration approach in survey theory and practice', Survey Methodology 33(2), 99-119.

19. Sarndal, Carl-Erik, Swensson, B. & Wretman, J. (2003), Model assisted survey sampling, Springer.

20. Tillé, Y. & Matei, A. (2013), sampling: Survey Sampling. R package version 2.6. *http://CRAN.R-project.org/packagesampling

[Recibido en enero de 2016. Aceptado en mayo de 2016]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n2a08,
    AUTHOR  = {Gutiérrez Rojas, Hugo Andrés and Zhang, Hanwen and Rodríguez, Nelson Andrés},
    TITLE   = {{The Performance of Multivariate Calibration on Ratios, Means and Proportions}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {2},
    pages   = {281-305}
}

References

Blais, A., Massicotte, L. & Dobrzynska, A. (1997), ‘Direct presidential elections: a world summary’, Electoral Studies 16(4), 441–455.

Bouton, L. & Gratton, G. (2015), ‘Majority runoff elections: Strategic voting and duverger’s hypothesis’, Theoretical Economics 10, 283–314.

Brewer, K. R. W. (1999), ‘Cosmetic calibration with unequal probability sampling’, Survey Methodology 25(2), 205–212.

Deville, J.-C. & Särndal, C.-E. (1992), ‘Calibration estimators in survey sampling’, Journal of the American statistical Association 87(418), 376–382.

Elkasabi, M. A., Heeringa, S. G. & Lepkowski, J. M. (2015), ‘Joint calibration estimator for dual frame surveys’, Statistics in Transition 16(1), 7–36.

Estevao, V. M. & Särndal, C. E. (2004), ‘Borrowing Strength Is Not the Best Technique Within a Wide Class of Design-Consistent Domain Estimators’, Journal of Official Statistics 20(4), 645–669.

Estevao, V. M. & Särndal, C.-E. (2006), ‘Survey estimates by calibration on complex auxiliary information’, International Statistical Review 74(2), 127–147.

Estevao, V. M., Särndal, C.-E. & Sautory, O. (2000), ‘A functional form approach to calibration’, Journal of Official Statistics 16, 379–399.

Kim, J. K. & Park, M. (2010), ‘Calibration estimation in survey sampling’, International Statistical Review 78(1), 21–39.

Kim, J.-M., Sungur, E. A. & Heo, T.-Y. (2007), ‘Calibration approach estimators in stratified sampling’, Statistics & Probability Letters 77(1), 99–103.

Kott, P. S. (2003), ‘A practical use for instrumental-variable calibration’, Journal of Official Statistics 19(3), 265–272.

Kott, P. S. (2004), ‘Comment on Demnati and Rao: Linarization variance estimators for survey data’, Survey Methodology 30, 27–28.

Krapavickaite, D. & Plikusas, A. (2005), ‘Estimation of a ratio in the finite population’, Informatica 16(3), 347–364.

Lesage, E. (2011), ‘The use of estimating equations to perform a calibration on complex parameters’, Survey methodology 37(1), 103–108.

Park, S. & Kim, J. K. (2014), ‘Instrumental-variable calibration estimation in survey sampling’, Statistica Sinica 24, 1001–1015.

Pérez-Liñán, A. (2006), ‘Evaluating presidential runoff elections’, Electoral Studies 25(1), 129–146.

Plikusas, A. (2006), Non-linear calibration, in ‘Proceedings, Workshop on survey sampling’, Venspils, Latvia. Riga: Central Statistical Bureau of Latvia.

R Development Core Team (2007), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *http://www.R-project.org

Särndal, C. E. (2007), ‘The calibration approach in survey theory and practice’, Survey Methodology 33(2), 99–119.

Särndal, C.-E., Swensson, B. & Wretman, J. (2003), Model assisted survey sampling, Springer.

Tillé, Y. & Matei, A. (2013), sampling: Survey Sampling. R package version 2.6. *http://CRAN.R-project.org/package=sampling

How to Cite

APA

Gutiérrez, H. A., Zhang, H. and Rodríguez, N. A. (2016). The Performance of Multivariate Calibration on Ratios, Means and Proportions. Revista Colombiana de Estadística, 39(2), 281–305. https://doi.org/10.15446/rce.v39n2.55424

ACM

[1]
Gutiérrez, H.A., Zhang, H. and Rodríguez, N.A. 2016. The Performance of Multivariate Calibration on Ratios, Means and Proportions. Revista Colombiana de Estadística. 39, 2 (Jul. 2016), 281–305. DOI:https://doi.org/10.15446/rce.v39n2.55424.

ACS

(1)
Gutiérrez, H. A.; Zhang, H.; Rodríguez, N. A. The Performance of Multivariate Calibration on Ratios, Means and Proportions. Rev. colomb. estad. 2016, 39, 281-305.

ABNT

GUTIÉRREZ, H. A.; ZHANG, H.; RODRÍGUEZ, N. A. The Performance of Multivariate Calibration on Ratios, Means and Proportions. Revista Colombiana de Estadística, [S. l.], v. 39, n. 2, p. 281–305, 2016. DOI: 10.15446/rce.v39n2.55424. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/55424. Acesso em: 28 mar. 2025.

Chicago

Gutiérrez, Hugo Andrés, Hanwen Zhang, and Nelson Andrés Rodríguez. 2016. “The Performance of Multivariate Calibration on Ratios, Means and Proportions”. Revista Colombiana De Estadística 39 (2):281-305. https://doi.org/10.15446/rce.v39n2.55424.

Harvard

Gutiérrez, H. A., Zhang, H. and Rodríguez, N. A. (2016) “The Performance of Multivariate Calibration on Ratios, Means and Proportions”, Revista Colombiana de Estadística, 39(2), pp. 281–305. doi: 10.15446/rce.v39n2.55424.

IEEE

[1]
H. A. Gutiérrez, H. Zhang, and N. A. Rodríguez, “The Performance of Multivariate Calibration on Ratios, Means and Proportions”, Rev. colomb. estad., vol. 39, no. 2, pp. 281–305, Jul. 2016.

MLA

Gutiérrez, H. A., H. Zhang, and N. A. Rodríguez. “The Performance of Multivariate Calibration on Ratios, Means and Proportions”. Revista Colombiana de Estadística, vol. 39, no. 2, July 2016, pp. 281-05, doi:10.15446/rce.v39n2.55424.

Turabian

Gutiérrez, Hugo Andrés, Hanwen Zhang, and Nelson Andrés Rodríguez. “The Performance of Multivariate Calibration on Ratios, Means and Proportions”. Revista Colombiana de Estadística 39, no. 2 (July 1, 2016): 281–305. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/55424.

Vancouver

1.
Gutiérrez HA, Zhang H, Rodríguez NA. The Performance of Multivariate Calibration on Ratios, Means and Proportions. Rev. colomb. estad. [Internet]. 2016 Jul. 1 [cited 2025 Mar. 28];39(2):281-305. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/55424

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