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Estimating Multilevel Models on Data Streams

Author

Listed:
  • L. Ippel

    (Maastricht University)

  • M. C. Kaptein

    (Tilburg University)

  • J. K. Vermunt

    (Tilburg University)

Abstract

Social scientists are often faced with data that have a nested structure: pupils are nested within schools, employees are nested within companies, or repeated measurements are nested within individuals. Nested data are typically analyzed using multilevel models. However, when data sets are extremely large or when new data continuously augment the data set, estimating multilevel models can be challenging: the current algorithms used to fit multilevel models repeatedly revisit all data points and end up consuming much time and computer memory. This is especially troublesome when predictions are needed in real time and observations keep streaming in. We address this problem by introducing the Streaming Expectation Maximization Approximation (SEMA) algorithm for fitting multilevel models online (or “row-by-row”). In an extensive simulation study, we demonstrate the performance of SEMA compared to traditional methods of fitting multilevel models. Next, SEMA is used to analyze an empirical data stream. The accuracy of SEMA is competitive to current state-of-the-art methods while being orders of magnitude faster.

Suggested Citation

  • L. Ippel & M. C. Kaptein & J. K. Vermunt, 2019. "Estimating Multilevel Models on Data Streams," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 41-64, March.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:1:d:10.1007_s11336-018-09656-z
    DOI: 10.1007/s11336-018-09656-z
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    References listed on IDEAS

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    1. Harvey Goldstein & Roderick McDonald, 1988. "A general model for the analysis of multilevel data," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 455-467, December.
    2. Liu, Z. & Almhana, J. & Choulakian, V. & McGorman, R., 2006. "Online EM algorithm for mixture with application to internet traffic modeling," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1052-1071, February.
    3. Kooreman, Peter & Scherpenzeel, Annette, 2014. "High frequency body mass measurement, feedback, and health behaviors," Economics & Human Biology, Elsevier, vol. 14(C), pages 141-153.
    4. Ippel, L. & Kaptein, M.C. & Vermunt, J.K., 2016. "Estimating random-intercept models on data streams," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 169-182.
    5. Olivier Cappé & Eric Moulines, 2009. "On‐line expectation–maximization algorithm for latent data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 593-613, June.
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