Improving the representativeness of a simple random samplean optimization model and its application to the Continuous Sample of Working Lives

  1. Vicente Nuñez-Antón 1
  2. Juan Manuel Pérez-Salamero González 2
  3. Marta Regúlez-Castillo 1
  4. Carlos Vidal-Meliá 2
  1. 1 Universidad del País Vasco/Euskal Herriko Unibertsitatea
    info

    Universidad del País Vasco/Euskal Herriko Unibertsitatea

    Lejona, España

    ROR https://ror.org/000xsnr85

  2. 2 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

Revista:
Documentos de Trabajo (ICAE)

ISSN: 2341-2356

Any de publicació: 2019

Número: 20

Pàgines: 1-30

Tipus: Document de treball

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Altres publicacions en: Documentos de Trabajo (ICAE)

Resum

This paper develops an optimization model for selecting a large subsample that improves the representativeness of a simple random sample previously obtained from a population larger than the population of interest. The problem formulation involves convex mixed-integer nonlinear programming (convex MINLP) and is therefore NP-hard. However, the solution is found by maximizing the “constant of proportionality” – in other words, maximizing the size of the subsample taken from a stratified random sample with proportional allocation – and restricting it to a p-value high enough to achieve a good fit to the population of interest using Pearson’s chi-square goodness-of-fit test. The beauty of the model is that it gives the user the freedom to choose between a larger subsample with a poorer fit and a smaller subsample with a better fit. The paper also applies the model to a real case: The Continuous Sample of Working Lives (CSWL), which is a set of anonymized microdata containing information on individuals from Spanish Social Security records. Several waves (2005-2017) are first examined without using the model and the conclusion is that they are not representative of the target population, which in this case is people receiving a pension income. The model is then applied and the results prove that it is possible to obtain a large dataset from the CSWL that (far) better represents the pensioner population for each of the waves analysed.

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Informació de finançament

We gratefully acknowledge the financial support from the Ministerio de Economía y Competitividad (Spain) and the Basque Government for projects ECO2015-65826-P and IT 793-13 respectively, and Ministerio de Economía y Competitividad, Agencia Estatal de Investigación (AEI), Fondo Europeo de Desarrollo Regional (FEDER), the Department of Education of the Basque Government (UPV/EHU Econometrics Research Group), and Universidad del País Vasco UPV/EHU under research grants MTM2016-74931-P (AEI/FEDER, UE), IT-642-13 and UFI11/03.

Finançadors

Referències bibliogràfiques

  • Baillargeon, S., & Rivest, L. P. (2009). A general algorithm for univariate stratification. International Statistical Review, 77(3), 331-344.
  • Berkson, J. (1938). Some difficulties of interpretation encountered in the application of the Chi-Square Test. Journal of the American Statistical Association, 33(203), 526-536.
  • Bonami, P., Kilinç, M., & Linderoth. J. (2012). Algorithms and software for convex mixed integer nonlinear programs. In J. Lee & S. Leyferr (Eds.), Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154 (pp. 1-39). New York: Springer.
  • Bowley, A. L. (1926). Measurement of precision attained in sampling. Bulletin of the International Statistical Institute 22(1), 6-62.
  • Cochran, W. G. (1977). Sampling Techniques. New York: John Wiley.
  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Hillsdale. NJ: Erlbaum.
  • D’Ambrosio, C., & Lodi, A. (2013). Mixed integer nonlinear programming tools: an updated practical overview. Annals of Operations Research, 204(1), 301-320.
  • De Moura Brito, J. A., Do Nascimento Silva, P. L., Silva Semaan, G., & Maculan, N. (2015). Integer programming formulations applied to optimal allocation in stratified sampling. Survey Methodology, 41(2), 427-442.
  • DGOSS (2006-2018). Muestra Continua de Vidas Laborales 2005-2017. Madrid: Dirección General de Ordenación de la Seguridad Social. Ministerio de Trabajo, Migraciones y Seguridad Social.
  • Díaz-García, J. A., & Ramos-Quiroga, R. (2012). Optimum allocation in multivariable stratified random sampling: stochastic matrix mathematical programming. Statistica Neerlandica, 66(4), 492-511.
  • Díaz-García, J. A., & Ramos-Quiroga, R. (2014). Optimum allocation in multivariable stratified random sampling: a modified Prékopa’s approach. Journal of Mathematical Modelling and Algorithms, 13, 315-330.
  • Grafström, A., & Schelin, L. (2014). How to select representative samples. Scandinavian Journal of Statistics, 41, 277 –290.
  • Gupta, N., Ali, I., & Bari, A. (2014). An optimal chance constraint multivariate stratified sampling design using auxiliary information. Journal of Mathematical Modelling and Algorithms in Operations Research, 13(3), 341-352.
  • Gupta, N., Sana Ifthekar, S., & Bari, A. (2012). Fuzzy goal programming approach to solve non-linear bi-level programming problem in stratified double sampling design in presence of non-response. International Journal of Scientific & Engineering Research, 3(10), 1-9.
  • INSS (2006-14). Informes Estadísticos 2005-2013. Madrid: Instituto Nacional de la Seguridad Social. Secretaría de Estado de la Seguridad Social. Ministerio de Trabajo, Migraciones y Seguridad Social.
  • INSS (2006-18). Informes Estadísticos 2005-2017. Madrid: Instituto Nacional de la Seguridad Social. Secretaría de Estado de la Seguridad Social. Ministerio de Trabajo, Migraciones y Seguridad Social.
  • Kontopantelis, E. (2013). A greedy algorithm for representative sampling: repsample in Stata. Journal of Statistical Software, 56, 1-18.
  • Kruskall, W., & Mosteller, F. (1979a). Representative sampling, I. International Statistical Review, 47(1), 13-24.
  • Kruskall, W., & Mosteller, F. (1979b). Representative sampling, II: scientific literature. excluding statistics. International Statistical Review, 47(2), 111-127.
  • Kruskall, W., & Mosteller, F. (1979c). Representative sampling, III: The Current Statistical Literature. International Statistical Review, 47(3), 245-265.
  • Kruskall, W., & Mosteller, F. (1980). Representative sampling, IV: the history of the Concept in Statistics. 1895-1939. International Statistical Review, 48(2), 169- 195.
  • Lin, M., Lucas, H. C., & Shmieli, G. (2013). Research commentary: too big to fail. Large samples and the p-value Problem. Information Systems Research, 24(4), 906-917.
  • MESS (2018). MCVL. Muestra Continua de Vidas Laborales. Guía del contenido. Estadísticas. Presupuestos y Estudios. Estadísticas. Muestra Continua de Vidas Laborales. Documentación MCVL. http://www.seg-social.es/wps/wcm/connect/wss/320b09c6-dc33-42be-b532- 08880e618742/MCVLGuia20180725.pdf?MOD=AJPERES&CVID= (accessed 11 Sep 2018).
  • Neyman, J. (1934). On the two different aspects of the representative method: The method of representative sampling and the method of purposive sampling. Journal of the Royal Statistical Society, 97(4), 558-625.
  • Nuñez-Antón, V., Pérez-Salamero González, J. M., Regúlez-Castillo, M., VenturaMarco, M., & Vidal-Meliá, C. (2019). Automatic regrouping of strata in the goodness-of-fit chi-square test. SORT, 43(1).In Press.
  • Olsen. A.;Hudson, R. (2009). Social Security Administration’s Master Earnings File: background information. Social Security Bulletin, 69(3), 29-45.
  • Omair. A. (2014). Sample size estimation and sampling techniques for selecting a representative sample. Journal of Health Specialties, 2(4), 142-147.
  • Pérez-Salamero González, J. M., Regúlez-Castillo, M., & Vidal-Meliá, C. (2016). Análisis de la representatividad de la MCVL: el caso de las prestaciones del sistema público de pensiones. Hacienda Pública Española, 217(2), 67–130.
  • Pérez-Salamero González, J. M., Regúlez-Castillo, M., & Vidal-Meliá. C. (2017). The continuous sample of working lives: improving its representativeness. SERIEs, 8(1), 43-95.
  • Ramsey, C. A., & Hewitt, A. D. (2005). A Methodology for assessing sample representativeness. Environmental Forensics, 6, 71–75.
  • Särndal, C. E., Swensson, B., & Wretman, J. (1992). Model Assisted Survey Sampling. Springer Series in Statistics. New York: Springer Verlag.
  • Smith, C. (1989). The Social Security Administration's Continuous Work History Sample. Social Security Bulletin, 52(10), 20–28.
  • Valliant, R., & Gentle, J. E. (1997). An application of mathematical programming to sample allocation. Computational Statistics & Data Analysis, 25(3), 337-360.
  • Valliant, R., Dever, J., & Kreuter, F. (2013). Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences, 51. New York: Springer.
  • Wang, C. (1993). Sense and Nonsense of Statistical Inference: Controversy, Misuse and Subtlety. New York: Marcel Dekker.
  • Zweimüller, J., Winter-Ebmer, R., Lalive, R., Kuhn, A., Wuellrich, J.P., Ruf, O., & Büchi, S. (2009). Austrian Social Security Database. IEW - Working Papers, 410. Institute for Empirical Research in Economics - University of Zurich.
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