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

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 (henceforth GAMM), using factor smooths to capture trial-to-trial dependencies. From a series of simulations using sine waves representing such dependencies, Thul et al. (2020) draw the conclusion that GAMMs are inappropriate for between-subject designs. They argue that effects of experimental time can be safely ignored as noise in statistical analyses when using linear mixed models (LMM). We address the questions raised by Thul et al. (2020), who clearly demonstrated that problems can arise when using factor smooths in combination with factorial designs. We show that the problem they reported 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 a series of simulation studies implementing by-subject longitudinal effects. Simulations included both sinusoid time-varying effects (following Thul et al. 2020) and random longitudinal effects. The maximal LMM emerges as slightly conservative compared to GAMMs, and GAMMs provide estimated coefficients that are less variable across simulation runs. We also report analyses of two experimental datasets in which time-varying effects interact with predictors of theoretical interest. We conclude that GAMMs are an excellent and reliable tool for understanding chronometric data with time-varying effects, for both blocked and unblocked experimental designs.