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Multiple system estimation using covariates having missing values and measurement error: Estimating the size of the Māori population in New Zealand

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  • Peter G. M. van der Heijden
  • Maarten Cruyff
  • Paul A. Smith
  • Christine Bycroft
  • Patrick Graham
  • Nathaniel Matheson‐Dunning

Abstract

We investigate the use of two or more linked lists, for both population size estimation and the relationship between variables appearing on all or only some lists. This relationship is usually not fully known because some individuals appear in only some lists, and some are not in any list. These two problems have been solved simultaneously using the EM algorithm. We extend this approach to estimate the size of the indigenous Māori population in New Zealand, leading to several innovations: (1) the approach is extended to four lists (including the population census), where the reporting of Māori status differs between registers; (2) some individuals in one or more lists have missing ethnicity, and we adapt the approach to handle this additional missingness; (3) some lists cover subsets of the population by design. We discuss under which assumptions such structural undercoverage can be ignored and provide a general result; (4) we treat the Māori indicator in each list as a variable measured with error, and embed a latent class model in the multiple system estimation to estimate the population size of a latent variable, interpreted as the true Māori status. Finally, we discuss estimating the Māori population size from administrative data only. Supplementary materials for our article are available online.

Suggested Citation

  • Peter G. M. van der Heijden & Maarten Cruyff & Paul A. Smith & Christine Bycroft & Patrick Graham & Nathaniel Matheson‐Dunning, 2022. "Multiple system estimation using covariates having missing values and measurement error: Estimating the size of the Māori population in New Zealand," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 156-177, January.
    • Handle: RePEc:bla:jorssa:v:185:y:2022:i:1:p:156-177
    DOI: 10.1111/rssa.12731
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    References listed on IDEAS

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    1. Elena Stanghellini & Peter G. M. van der Heijden, 2004. "A Multiple-Record Systems Estimation Method that Takes Observed and Unobserved Heterogeneity into Account," Biometrics, The International Biometric Society, vol. 60(2), pages 510-516, June.
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    3. Di Cecco Davide & Di Zio Marco & Filipponi Danila & Rocchetti Irene, 2018. "Population Size Estimation Using Multiple Incomplete Lists with Overcoverage," Journal of Official Statistics, Sciendo, vol. 34(2), pages 557-572, June.
    4. Jason M. Sutherland & Carl James Schwarz & Louis-Paul Rivest, 2007. "Multilist Population Estimation with Incomplete and Partial Stratification," Biometrics, The International Biometric Society, vol. 63(3), pages 910-916, September.
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    6. Laura Boeschoten & Ton de Waal & Jeroen K. Vermunt, 2019. "Estimating the number of serious road injuries per vehicle type in the Netherlands by using multiple imputation of latent classes," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1463-1486, October.
    7. Boeschoten Laura & Oberski Daniel & de Waal Ton, 2017. "Estimating Classification Errors Under Edit Restrictions in Composite Survey-Register Data Using Multiple Imputation Latent Class Modelling (MILC)," Journal of Official Statistics, Sciendo, vol. 33(4), pages 921-962, December.
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