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Statistical properties of Multiscale Regression Analysis: Simulation and application to human postural control

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  • Likens, Aaron D.
  • Amazeen, Polemnia G.
  • West, Stephen G.
  • Gibbons, Cameron T.

Abstract

Multiscale Regression Analysis (MRA) is a promising new tool for the analysis of bivariate time series that is based on Detrended Fluctuation Analysis (DFA) and Ordinary Least Squares (OLS) regression. The method was developed within the economics and environmental science literatures (Kristoufek, 2015, 2018; Kristoufek and Ferreira, 2018) and is beginning to be applied in other scientific domains. To date, however, no systematic studies have investigated the behavior of the estimator with respect to short time series. This paper fills that gap by assessing the performance of the MRA estimator using time series with varying length, distribution, and structure (e.g., autocorrelation, stationarity). Simulations show that MRA performs well under many circumstances with as few as 512 observations. Linear and quadratic time trends contribute considerable systematic bias; however, using a detrending polynomial of order ≥ 2 effectively attenuates time trend associated deviations from expected values. We apply MRA to a previously published dataset in order to explore the relationship that emerges between body segments during an act of quiet standing. Results suggest that the velocity of the hip asymptotically depends on velocity of the ankle. In contrast, ankle velocity was a much weaker predictor of shoulder velocity. We conclude by providing suggestions for best practice and future model development.

Suggested Citation

  • Likens, Aaron D. & Amazeen, Polemnia G. & West, Stephen G. & Gibbons, Cameron T., 2019. "Statistical properties of Multiscale Regression Analysis: Simulation and application to human postural control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    • Handle: RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119309331
    DOI: 10.1016/j.physa.2019.121580
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    Citations

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    Cited by:

    1. Tilfani, Oussama & Kristoufek, Ladislav & Ferreira, Paulo & El Boukfaoui, My Youssef, 2022. "Heterogeneity in economic relationships: Scale dependence through the multivariate fractal regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    2. Bo Wen & Ruiyang Li & Xue Zhao & Shuang Ren & Yali Chang & Kexin Zhang & Shan Wang & Guiyi Guo & Xujun Zhu, 2021. "A Quadratic Regression Model to Quantify Plantation Soil Factors That Affect Tea Quality," Agriculture, MDPI, vol. 11(12), pages 1-12, December.
    3. Barreto, Ikaro Daniel de Carvalho & Dore, Luiz Henrique & Stosic, Tatijana & Stosic, Borko D., 2021. "Extending DFA-based multiple linear regression inference: Application to acoustic impedance models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    4. Kelty-Stephen, Damian G. & Furmanek, Mariusz P. & Mangalam, Madhur, 2021. "Multifractality distinguishes reactive from proactive cascades in postural control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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