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.

翻译：Thul等人(2020年)呼吁注意在用通用添加混合模型(此后的GAMM)分析用于特定要素设计的计时实验实施具体要素设计时出现的问题。Thul等人(2020年)通过一系列使用正弦波的模拟来得出这种依赖性的结论,即GAMM对于对象之间设计不合适。他们认为,使用线性混合模型(LMM)时,试验时间的影响可以安全地被忽略为统计分析中的噪音。我们讨论了Tul等人(202020年)提出的问题,他们清楚地表明,使用因子平稳与要素设计相结合时,可能会出现问题。我们表明,他们所报告的问题不会在使用正弦波时出现。此外,我们在使用 mgcv 组合中的因子平稳应用中发现了一个错误,从第1.8-36版开始,它们争辩说,当使用线性混合模型(LMMM)时,试验时间影响可以安全地被忽略为统计分析中的噪音。我们报告了一系列模拟研究,用长期影响进行模拟研究。模拟时,在模拟中,将正弦性时间效果和MMMMMM的模型模型模型模型模型模型模型模型模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型的模型,