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

Vicente Nuñez-Antón ^[1] ; Juan Manuel Pérez-Salamero González ^[2] ; Marta Regúlez-Castillo ^[1] ; Carlos Vidal-Meliá ^[2]
1. [1] Universidad del País Vasco/Euskal Herriko Unibertsitatea
  
  Universidad del País Vasco/Euskal Herriko Unibertsitatea
  
  Leioa, España
2. [2] Universitat de València
  
  Universitat de València
  
  Valencia, España
Localización: Documentos de Trabajo (ICAE), ISSN-e 2341-2356, Nº. 20, 2019, págs. 1-30
Idioma: inglés
Enlaces
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Resumen
- 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.