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Subsampling in Longitudinal Models

Author

Listed:
  • Ziyang Wang

    (University of Connecticut)

  • HaiYing Wang

    (University of Connecticut)

  • Nalini Ravishanker

    (University of Connecticut)

Abstract

For large scale data, subsampling methods are often used to approximate the full-data parameter estimates. An ideal subsampling method picks a small proportion of informative observations from the full data and produces an accurate approximate to the full-data estimate using much less computing power. Existing studies on subsampling methods focus on independent responses. This paper discusses subsampling methods for longitudinal data where observations within a block are correlated, and develops optimal subsampling methods to approximate the full-data maximum likelihood estimators of the model parameters. We first establish the conditional asymptotic distribution of the subsample estimator with general subsampling probabilities, and then derive the optimal subsampling method that minimizes the asymptotic mean squared error of the subsample estimator. To evaluate the finite sample performance of the proposed method, we provide results based on numerical experiments with simulated data.

Suggested Citation

  • Ziyang Wang & HaiYing Wang & Nalini Ravishanker, 2023. "Subsampling in Longitudinal Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10015-4
    DOI: 10.1007/s11009-023-10015-4
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    References listed on IDEAS

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    1. Yaqiong Yao & HaiYing Wang, 2019. "Optimal subsampling for softmax regression," Statistical Papers, Springer, vol. 60(2), pages 585-599, April.
    2. Jing Zhao & Chong Wang & Sarah C Totton & Jonah N Cullen & Annette M O’Connor, 2019. "Reporting and analysis of repeated measurements in preclinical animals experiments," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-18, August.
    3. Haiying Wang & Yanyuan Ma, 2021. "Optimal subsampling for quantile regression in big data," Biometrika, Biometrika Trust, vol. 108(1), pages 99-112.
    4. HaiYing Wang & Min Yang & John Stufken, 2019. "Information-Based Optimal Subdata Selection for Big Data Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 393-405, January.
    5. HaiYing Wang & Rong Zhu & Ping Ma, 2018. "Optimal Subsampling for Large Sample Logistic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 829-844, April.
    Full references (including those not matched with items on IDEAS)

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