Mixed-effects models in R, and a new tool for data simulation

Thu, Nov 26, 2020
New Tricks Seminars, Dept. Psychology, Lancaster University


Linear mixed-effects models (LMEMs) are used to account for variation within factors with multiple observations, such as participants, trials, items, channels, etc (for an earlier approach, see Clark, 1973). This variation is modelled in terms of random intercepts (e.g., overall variation per participant) as well as random slopes for the fixed effects (e.g., treatment effect per participant). These measures help reduce false positives and false negatives (Barr, Levy, Scheepers, & Tily, 2013), and the resulting models tend to be robust to violations of assumptions (Schielzeth et al., 2020). The use of LMEMs has grown over the past decade, under various implementation forms (Meteyard & Davies, 2020). In this talk, I will look over the rationale for LMEMs, and demonstrate how to fit them in R (Brauer, & Curtin, 2018; Luke, 2017). Challenges will also be covered. For instance, when using the widely-accepted ‘maximal’ approach, based on fitting all possible random effects for each fixed effect, models sometimes fail to find a solution, or ‘convergence’. Advice for the problem of nonconvergence will be demonstrated, based on the progressive lightening of the random effects structure (Singman & Kellen, 2017; for an alternative approach, especially with small samples, see Matuschek, Kliegl, Vasishth, Baayen, & Bates, 2017). At the end, on a different note, I will present a web application that facilitates data simulation for research and teaching (Bernabeu & Lynott, 2020).


Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68, 255–278. http://dx.doi.org/10.1016/j.jml.2012.11.001

Bernabeu, P., & Lynott, D. (2020). Web application for the simulation of experimental data (Version 1.0). Retrieved from https://github.com/pablobernabeu/Experimental-data-simulation

Brauer, M., & Curtin, J. J. (2018). Linear mixed-effects models and the analysis of nonindependent data: A unified framework to analyze categorical and continuous independent variables that vary within-subjects and/or within-items. Psychological Methods, 23(3), 389–411. https://doi.org/10.1037/met0000159

Clark, H. H. (1973). The language-as-fixed-effect fallacy: A critique of language statistics in psychological research. Journal of Verbal Learning and Verbal Behavior, 12(4), 335-359. https://doi.org/10.1016/S0022-5371(73)80014-3

Luke, S. G. (2017). Evaluating significance in linear mixed-effects models in R. Behavior Research Methods, 49(4), 1494–1502. https://doi.org/10.3758/s13428-016-0809-y

Matuschek, H., Kliegl, R., Vasishth, S., Baayen, H., & Bates, D. (2017). Balancing type 1 error and power in linear mixed models. Journal of Memory and Language, 94, 305–315. https://doi.org/10.1016/j.jml.2017.01.001

Meteyard, L., & Davies, R. A. (2020). Best practice guidance for linear mixed-effects models in psychological science. Journal of Memory and Language, 112, 104092. https://doi.org/10.1016/j.jml.2020.104092

Schielzeth, H., Dingemanse, N. J., Nakagawa, S., Westneat, D. F., Allegue, H, Teplitsky, C., Reale, 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, 00, 1– 12. https://doi.org/10.1111/2041-210X.13434

Singmann, H., & Kellen, D. (2019). An Introduction to Mixed Models for Experimental Psychology. In D. H. Spieler & E. Schumacher (Eds.), New Methods in Cognitive Psychology (pp. 4–31). Hove, UK: Psychology Press. http://singmann.org/download/publications/singmann_kellen-introduction-mixed-models.pdf

Pablo Bernabeu
Psychology PhD student and teaching assistant at Lancaster University

After doing a research master's, I became a PhD student and graduate teaching assistant in Psychology. I'm investigating how conceptual processing is supported by linguistic and sensorimotor brain systems. I use methods such as behavioural and electroencephalographic experiments, corpus analysis, statistics and programming.

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