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A stickiness coefficient for longitudinal data

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  • Gottlieb, Andrea
  • Müller, Hans-Georg

Abstract

In this paper, we introduce the stickiness coefficient, a summary statistic for time-course and longitudinal data, which is designed to characterize the time dynamics of such data. The stickiness coefficient provides a simple, intuitive and informative measure that captures key information contained in time-course data. Under the assumption that the data are generated by the trajectories of a smooth underlying stochastic process, the stickiness coefficient illuminates the relationship between the value of the process at one time with the value it assumes at another time via a single numeric measure. In particular, the stickiness coefficient summarizes the extent to which deviations from the mean trajectory tend to co-vary over time. The estimation scheme we propose will allow for estimation even in the case that the longitudinal data are sparsely observed at irregular times and may be corrupted by noise. We demonstrate an estimation procedure for the stickiness coefficient and establish asymptotic consistency as well as asymptotic convergence rates. We illustrate the resulting stickiness coefficient with some theoretical calculations as well as several economic and health related data examples.

Suggested Citation

  • Gottlieb, Andrea & Müller, Hans-Georg, 2012. "A stickiness coefficient for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4000-4010.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4000-4010
    DOI: 10.1016/j.csda.2012.03.009
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    References listed on IDEAS

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    1. Liu, Bitao & Müller, Hans-Georg, 2009. "Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 704-717.
    2. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    3. John A. Rice & Colin O. Wu, 2001. "Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, The International Biometric Society, vol. 57(1), pages 253-259, March.
    4. Daniel Gervini & Theo Gasser, 2004. "Self‐modelling warping functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 959-971, November.
    5. Wang, Shanshan & Jank, Wolfgang & Shmueli, Galit, 2008. "Explaining and Forecasting Online Auction Prices and Their Dynamics Using Functional Data Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 144-160, April.
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    Cited by:

    1. Andreas Kryger Jensen & Claus Thorn Ekstrøm, 2021. "Quantifying the trendiness of trends," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 98-121, January.

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