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Article published In:
The Mental Lexicon
Vol. 17:2 (2022) ► pp.178–212

A note on the modeling of the effects of experimental time in psycholinguistic experiments

| University of Tübingen
| University of Bristol
| University of Edinburgh
| University of Tübingen

Thul et al. (2020) called attention to problems that arise when chronometric experiments implementing specific factorial designs are analysed with the generalized additive mixed model (GAMM), using factor smooths to capture trial-to-trial dependencies. From a series of simulations incorporating such dependencies, they conclude that GAMMs are inappropriate for between-subject designs. They argue that in addition GAMMs come with too many modeling possibilities, and advise using the linear mixed model (LMM) instead. As clarified by the title of their paper, their conclusion is: “Using GAMMs to model trial-by-trial fluctuations in experimental data: More risks but hardly any benefit”.

We address the questions raised by Thul et al. (2020), who clearly demonstrated that problems can indeed arise when using factor smooths in combination with factorial designs. We show that the problem does not arise when using by-smooths. Furthermore, we have traced a bug in the implementation of factor smooths in the mgcv package, which will have been removed from version 1.8–36 onwards.

To illustrate that GAMMs now produce correct estimates, we report simulation studies implementing different by-subject longitudinal effects. The maximal LMM emerges as slightly conservative compared to GAMMs, and GAMMs provide estimated coefficients that can be less variable across simulation runs. We also discuss two datasets where time-varying effects interact with numerical predictors in a theoretically informative way.

Keywords: generalized additive mixed model, factor smooths, by smooths, factorial designs, time-varying effects, random effects, researcher degrees of freedom, replication
Article outline
  • 1.Introduction
  • 2.Sine waves
    • 2.1Sine waves with varying amplitudes
    • 2.2Sine waves with varying phase
  • 3.Power and Type-I error rate
    • 3.1Sine waves with varying absolute amplitude
    • 3.2Sine waves with varying phase
    • 3.3Simulations with the parameters of Thul et al. (2021)
    • 3.4From sine waves to random time-varying effects
  • 4.Interactions with time in experimental data
  • 5.Discussion
  • 6.Open practices statement
  • Acknowledgements
  • Notes
  • Mathematical notation
  • References
Available under the Creative Commons Attribution (CC BY) 4.0 license.

For any use beyond this license, please contact the publisher at [email protected].

Published online: 4 April 2022
DOI logo
https://doi.org/10.1075/ml.21012.baa
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