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Multilevel hierarchical Bayesian versus state space approach in time series small area estimation: the Dutch Travel Survey

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  • Oksana Bollineni‐Balabay
  • Jan van den Brakel
  • Franz Palm
  • Harm Jan Boonstra

Abstract

This study compares state space models (estimated with the Kalman filter with a frequentist approach to hyperparameter estimation) with multilevel time series models (based on the hierarchical Bayesian framework). The application chosen is the Dutch Travel Survey featuring small sample sizes and discontinuities caused by the survey redesigns. Both modelling approaches deliver similar point and variance estimates. Slight differences in model‐based variance estimates appear mostly in small‐scaled domains and are due to neglecting uncertainty around the hyperparameter estimates in the state space models, and to a lesser extent to skewness in the posterior distributions of the parameters of interest. The results suggest that the reduction in design‐based standard errors with the hierarchical Bayesian approach is over 50% at the provincial level, and over 30% at the national level.

Suggested Citation

  • Oksana Bollineni‐Balabay & Jan van den Brakel & Franz Palm & Harm Jan Boonstra, 2017. "Multilevel hierarchical Bayesian versus state space approach in time series small area estimation: the Dutch Travel Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1281-1308, October.
    • Handle: RePEc:bla:jorssa:v:180:y:2017:i:4:p:1281-1308
    DOI: 10.1111/rssa.12332
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    2. Krieg, Sabine & van den Brakel, Jan A., 2012. "Estimation of the monthly unemployment rate for six domains through structural time series modelling with cointegrated trends," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2918-2933.
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    4. Danny Pfeffermann & Anna Sikov & Richard Tiller, 2014. "Single- and two-stage cross-sectional and time series benchmarking procedures for small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 631-666, December.
    5. Oksana Bollineni-Balabay & Jan Brakel & Franz Palm, 2016. "Multivariate state space approach to variance reduction in series with level and variance breaks due to survey redesigns," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 377-402, February.
    6. Jan A. Brakel & Sabine Krieg, 2016. "Small area estimation with state space common factor models for rotating panels," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 763-791, June.
    7. Pfeffermann, Danny, 1991. "Estimation and Seasonal Adjustment of Population Means Using Data from Repeated Surveys: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 177-177, April.
    8. Pfeffermann, Danny & Tiller, Richard, 2006. "Small-Area Estimation With StateSpace Models Subject to Benchmark Constraints," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1387-1397, December.
    9. Danny Pfeffermann & Anna Sikov & Richard Tiller, 2014. "Rejoinder on: Single- and two-stage cross-sectional and time series benchmarking procedures for small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 686-690, December.
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    Cited by:

    1. Harm Jan Boonstra & Jan van den Brakel & Sumonkanti Das, 2021. "Multilevel time series modelling of mobility trends in the Netherlands for small domains," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 985-1007, July.

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