Modeling Longitudinal Outcomes: A Contrast of Two Methods

in Journal of Motor Learning and Development
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  • 1 University of Utah
  • 2 Michigan State University
  • 3 Mary Free Bed Rehabilitation Hospital
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Background: Repeated measures analysis of variance (ANOVA) is frequently used to model longitudinal data but does not appropriately account for within-person correlations over time, does not explicitly model time, and cannot flexibly handle missing data. In contrast, mixed-effects regression addresses these limitations. In this commentary, we compare these two methods using openly available tools. Methods: We emulated a real developmental study of elite skiers, tracking national rankings from 2011 to 2018. We constructed unconditional models of time (establishing the “pattern” of change) and conditional models of time (identifying factors that affect change over time), and contrasted these models against comparable repeated measures ANOVAs. Results: Mixed-effects regression allowed for linear and non-linear modeling of the skiers’ longitudinal trajectories despite missing data. Missing data is still a concern in mixed-effects regression models, but in the present dataset missingness could be accounted for by skiers’ ages, satisfying the missing at random assumption. Discussion: Although ANOVA and mixed-effects regression are both suitable for time-series data, their applications differ. ANOVA will be most parsimonious when the research question focuses on group-level mean differences at arbitrary time points. However, mixed-effects regression is more suitable where time is inherently important to the outcome, and where individual differences are of interest.

Lohse is with the Department of Health, Kinesiology, and Recreation; and the Department of Physical Therapy and Athletic Training; Shen is with the Department of Population Health Sciences; University of Utah, Salt Lake City, UT. Kozlowski is with the Department of Epidemiology and Biostatistics, College of Human Medicine, Michigan State University, East Lansing, MI; and the John F. Butzer Center for Research and Innovation, Mary Free Bed Rehabilitation Hospital, Grand Rapids, MI.

Lohse (rehabinformatics@gmail.com) is corresponding author.
  • Angell, R.M., Butterfield, S.A., Tu, S., Loovis, E.M., Mason, C.A., & Nightingale, C.J. (2018). Children’s throwing and striking: A longitudinal study. Journal of Motor Learning and Development, 6(2), 315332. doi:10.1123/jmld.2017-0026

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 148. doi:10.18637/jss.v067.i01

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brysbaert, M., & Stevens, M. (2018). Power analysis and effect size in mixed effects models: A tutorial. Journal of Cognition, 1(1), 9. PubMed ID: 31517183 doi:10.5334/joc.10

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cantin, N., Ryan, J., & Polatajko, H.J. (2014). Impact of task difficulty and motor ability on visual-motor task performance of children with and without developmental coordination disorder. Human Movement Science, 34, 217232. doi:10.1016/j.humov.2014.02.006

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Curran, P.J., Obeidat, K., & Losardo, D. (2010). Twelve frequently asked questions about growth curve modeling. Journal of Cognition and Development, 11(2), 121136. PubMed ID: 21743795 doi:10.1080/15248371003699969

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dixon, P.C., Smith, T., Taylor, M.J.D., Jacobs, J.V., Dennerlein, J.T., & Schiffman, J.M. (2019). Effect of walking surface, late-cueing, physiological characteristics of aging, and gait parameters on turn style preference in healthy, older adults. Human Movement Science, 66, 504510. doi:10.1016/j.humov.2019.06.002

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Enders, C.K. (2011). Missing not at random models for latent growth curve analyses. Psychological Methods, 16(1), 116. PubMed ID: 21381816 doi:10.1037/a0022640

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fawver, B., Cowan, R.L., DeCouto, B., Lohse, K.R., Podlog, L., & Williams, A.M. (2020). Psychological characteristics, sport engagement, and performance in alpine skiers. Psychology of Sport and Exercise, 47, 101616. doi:10.1016/j.psychsport.2019.101616

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garcia, T.P., & Marder, K. (2017). Statistical approaches to longitudinal data analysis in neurodegenerative diseases: Huntington’s disease as a model. Current Neurology and Neuroscience Reports, 17(2), 14. PubMed ID: 28229396 doi:10.1007/s11910-017-0723-4

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gelman, A., & Hill, J. (2007). Data analysis using regression and hierarchical/multilevel models. New York, NY: Cambridge.

  • Green, B.F., & Tukey, J.W. (1960). Complex analyses of variance: General problems. Psychometrika, 25(2), 127152.

  • Greenhouse, S.W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95112. doi:10.1007/BF02289823

  • Hart, T., Kozlowski, A.J., Whyte, J., Poulsen, I., Kristensen, K., Nordenbo, A., & Heinemann, A.W. (2014). Functional recovery after severe traumatic brain injury: An individual growth curve approach. Archives of Physical Medicine and Rehabilitation, 95(11), 21032110. PubMed ID: 25010537 doi:10.1016/j.apmr.2014.07.001

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hendry, D.T., Williams, A.M., & Hodges, N.J. (2018). Coach ratings of skills and their relations to practice, play and successful transitions from youth-elite to adult-professional status in soccer. Journal of Sports Sciences, 36(17), 20092017. PubMed ID: 29400614 doi:10.1080/02640414.2018.1432236

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hodges, N.J., Kerr, T., Starkes, J.L., Weir, P.L., & Nananidou, A. (2004). Predicting performance times from deliberate practice hours for triathletes and swimmers: What, when, and where is practice important? Journal of Experimental Psychology: Applied, 10(4), 219237. PubMed ID: 15598120 doi:10.1037/1076-898X.10.4.219

    • Search Google Scholar
    • Export Citation
  • Judd, C.M., Westfall, J., & Kenny, D.A. (2012). Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem. Journal of Personality and Social Psychology, 103(1), 5469. PubMed ID: 22612667 doi:10.1037/a0028347

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kenward, M.G., & Roger, J.H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53, 983997. doi:10.2307/2533558

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kozlowski, A.J., Pretz, C.R., Dams-O’Connor, K., Kreider, S., & Whiteneck, G. (2013). An introduction to applying individual growth curve models to evaluate change in rehabilitation: A National Institute on Disability and Rehabilitation Research Traumatic Brain Injury Model Systems report. Archives of Physical Medicine and Rehabilitation, 94(3), 589596. PubMed ID: 22902887 doi:10.1016/j.apmr.2012.08.199

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lindstrom, M.J., & Bates, D.M. (1990). Nonlinear mixed effects models for repeated measures data. Biometrics, 46(3), 673687. PubMed ID: 2242409 doi:10.2307/2532087

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Long, J.D. (2012). Longitudinal data analysis for the behavioral sciences using R. Thousand Oaks, CA: Sage.

  • McClelland, G.H., Lynch, J.G., Jr., Irwin, J.R., Spiller, S.A., & Fitzsimons, G.J. (2015). Median splits, Type II errors, and false-positive consumer psychology: Don’t fight the power. Journal of Consumer Psychology, 25(4), 679689. doi:10.1016/j.jcps.2015.05.006

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mirman, D. (2014). Growth curve analysis and visualization using R (pp. 109112). Boca Raton, FL: CRC Press.

  • Molenberghs, G., & Verbeke, G. (2001). A review on linear mixed models for longitudinal data, possibly subject to dropout. Statistical Modelling, 1(4), 235269. doi:10.1177/1471082X0100100402

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pinheiro, J., & Bates, D. (2006). Mixed-effects models in S and S-PLUS. New York, NY: Springer Science & Business Media.

  • Raudenbush, S.W., & Bryk, A.S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage.

  • R Core Team. (2019). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.R-project.org/

    • Search Google Scholar
    • Export Citation
  • Singer, J.D., & Willett, J.B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford, UK: Oxford University Press.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vrieze, S.I. (2012). Model selection and psychological theory: a discussion of the differences between the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Psychological Methods, 17(2), 228243. PubMed ID: 22309957 doi:10.1037/a0027127

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Westfall, J., Kenny, D.A., & Judd, C.M. (2014). Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli. Journal of Experimental Psychology: General, 143(5), 20202045. doi:10.1037/xge0000014

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wickham, H. (2016). ggplot2: Elegant graphics for data analysis. New York, NY: Springer-Verlag.

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