Consequences of power transforms as a statistical solution in linear mixed-effects models of chronometric data

Abstract

Power transforms have been increasingly used in linear mixed-effects models (LMMs) of chronometric data (e.g., response times [RTs]) as a statistical solution to preempt violating the assumption of residual normality. However, differences in results between LMMs fit to raw RTs and transformed RTs have reignited discussions on issues concerning the transformation of RTs. Here, we analyzed three word-recognition megastudies and performed Monte Carlo simulations to better understand the consequences of transforming RTs in LMMs. Within each megastudy, transforming RTs produced different fixed- and random-effect patterns; across the megastudies, RTs were optimally normalized by different power transforms, and results were more consistent among LMMs fit to raw RTs. Moreover, the simulations showed that LMMs fit to optimally normalized RTs had greater power for main effects in smaller samples, but that LMMs fit to raw RTs had greater power for interaction effects as sample sizes increased, with negligible differences in Type I error rates between the two models. Based on these results, LMMs should be fit to raw RTs when there is no compelling reason beyond nonnormality to transform RTs and when the interpretive framework mapping the predictors and RTs treats RT as an interval scale.

Young Learners’ Processing of Multimodal Input and Its Impact on Reading Comprehension

“…Shapiro-Wilk tests confirmed significant deviations from normality for Dwell Time %: W = .76, p < .0001; Fixation Count %: W = .77, p < .0001; and Average Fixation Duration: W = .98, p < .0001. There is, however, marked disagreement as to the importance of parametric assumptions (e.g., McCulloch & Neuhaus, 2011), with evidence pointing to the relative robustness of linear mixed models to violations of normality (Arnau et al, 2013), and debate as to the cost-benefits of data transformations to address issues of nonnormality in terms of interpretability of the effects (Liceralde & Gordon, 2018). While some authors have recommended alternative statistical approaches (e.g., GLMMs; Lo & Andrews, 2015), particularly in cases of small sample sizes (Arnau et al, 2013), in this instance, we have instead opted to fit a robust linear mixed model to the data using the robustlmm package (v 2.3; Koller, 2016) as a check for our analysis.…”

Do effects of visual contrast and font difficulty on readers’ eye movements interact with effects of word frequency or predictability?

“…A power transform such as the log transform will often solve this problem, as the distribution of log fixation durations will usually be approximately normal. Thus, many researchers (e.g., Baayen, 2008) have recommended such transformations when using mixed-effects models for statistical analysis of RTs (though see Liceralde & Gordon, 2018, for an argument that the case for transformation based on violations of normality is less clear than has been assumed).…”

“…Thus, data transformation, in the present case, may be statistically appropriate (cf. Liceralde & Gordon, 2018), but it is interpretively problematic. To address this issue, we present linear mixed effects models of raw fixation duration measures, but also conduct the same analyses on log transformed data, and report any cases where the two sets of models differ in their patterns of significance.…”

The coarticulation-duration relationship in early Quechua speech

“…The choice to fit gamma GLMMs, as opposed to log-normalizing Sequence duration and fitting linear mixed models, reflects some recent suggestions in cognitive psychology to avoid data transformation, even for commonlytransformed variables such as time, duration, or response time, to facilitate between-study comparison (Liceralde 2018;Lo and Andrews 2015). However, there is not yet a consensus in the literature on the use of transformed versus untransformed variables.…”