Modeling Retest Effects in a Longitudinal Measurement Burst Study of Memory


Longitudinal designs must deal with the confound between increasing age and increasing task experience (i.e., retest effects). Most existing methods for disentangling these factors rely on large sample sizes and are impractical for smaller scale projects. Here, we show that a measurement burst design combined with a model of retest effects can be used to study age-related change with modest sample sizes. A combined model of age-related change and retest-related effects was developed. In a simulation experiment, we show that with sample sizes as small as n = 8, the model can reliably detect age effects of the size reported in the longitudinal literature while avoiding false positives when there is no age effect. We applied the model to data from a measurement burst study in which eight subjects completed a burst of seven sessions of free recall every year for 5 years. Six additional subjects completed a burst only in years 1 and 5. They should, therefore, have smaller retest effects but equal age effects. The raw data suggested slight improvement in memory over 5 years. However, applying the model to the yearly-testing group revealed that a substantial positive retest effect was obscuring stability in memory performance. Supporting this finding, the control group showed a smaller retest effect but an equal age effect. Measurement burst designs combined with models of retest effects allow researchers to employ longitudinal designs in areas where previously only cross-sectional designs were feasible.

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Data Accessibility

The data reported in this study as well as code for fitting the model can be freely accessed at


  1. 1.

    Rather than fitting each subject separately, as we have done, one could instead fit all subjects simultaneously within a hierarchical model in which hyper-parameters specify the distributions and covariance structure of the individual-level parameters. For applications where the the nature of the distributions (e.g., Gaussian vs. exGaussian, unimodal vs. bimodal, etc.) can be reasonably hypothesised a priori, such a hierarchical approach would be ideal. In situations where the nature of the distributions is unknown, fitting individual subjects and examining the resulting empirical distributions would be more appropriate.

  2. 2.

    We explored how the use of different fitting algorithms influenced power and false alarms. Fast heuristic algorithms (e.g., multistart, Ugray et al. 2007) provided slightly lower power and type I error rates whereas a slower but more exhaustive grid search provided higher power. We encourage researchers to consider this tradeoff when determining how to fit their own data.


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We thank Ada Aka, Elizabeth Crutchley, Patrick Crutchley, Kylie Hower, Joel Kuhn, Jonathan Miller, Logan O’Sullivan, and Isaac Pedisich for assistance conducting the study.


This work was supported by the National Institute on Aging at the National Institutes of Health (grant number AG048233) and the National Institute of Mental Health at the National Institutes of Health (grant number MH55687).

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Correspondence to M. Karl Healey.

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Broitman, A.W., Kahana, M.J. & Healey, M.K. Modeling Retest Effects in a Longitudinal Measurement Burst Study of Memory. Comput Brain Behav 3, 200–207 (2020).

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  • Free recall
  • Memory models
  • Stability
  • Aging
  • Practice effects