Residual errors not normally distributed

The residuals of the linear mixed-effects models in the three studies violated the assumption of normality. Even though linear mixed-effects models tend to be quite robust to deviations from normality (Knief & Forstmeier, 2021; Schielzeth et al., 2020), we sought to verify our results. To this end, we attempted to run robust models using two methods, neither of which worked. The methods are nonetheless described below.

Method A: robustlmm model

The first method drew on the R package ‘robustlmm’ v2.4-4 (Koller, 2016). To calculate the \(p\) values, we followed the procedure of Sleegers et al. (2021), but used the Kenward-Roger method instead of Satterthwaite (see Luke, 2017).


Fox, J. (2016). Generalized linear models. In Applied regression analysis and generalized linear models (Third Edition, pp. 418–472). SAGE.
Knief, U., & Forstmeier, W. (2021). Violating the normality assumption may be the lesser of two evils. Behavior Research Methods.
Koller, M. (2016). robustlmm: An R package for robust estimation of linear mixed-effects models. Journal of Statistical Software, 75(6), 1–24.
Lo, S., & Andrews, S. (2015). To transform or not to transform: Using generalized linear mixed models to analyse reaction time data. Frontiers in Psychology, 6, 1171.
Luke, S. G. (2017). Evaluating significance in linear mixed-effects models in R. Behavior Research Methods, 49(4), 1494–1502.
Schielzeth, H., Dingemanse, N. J., Nakagawa, S., Westneat, D. F., Allegue, H., Teplitsky, C., Réale, D., Dochtermann, N. A., Garamszegi, L. Z., & Araya‐Ajoy, Y. G. (2020). Robustness of linear mixed‐effects models to violations of distributional assumptions. Methods in Ecology and Evolution, 11(9), 1141–1152.
Singmann, H., Bolker, B., Westfall, J., Aust, F., & Ben-Shachar, M. S. (2021). afex: Analysis of factorial experiments.
Sleegers, W. W. A., Proulx, T., & van Beest, I. (2021). Pupillometry and hindsight bias: Physiological arousal predicts compensatory behavior. Social Psychological and Personality Science, 12(7), 1146–1154.

Pablo Bernabeu, 2022. Licence: CC BY 4.0.

Online book created using the R package bookdown.