Understanding Mixed-Effects Models Through Data Simulation
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Abstract
Experimental designs that sample both subjects and stimuli from a larger population need to account for random effects of both subjects and stimuli using mixed-effects models. However, much of this research is analyzed using analysis of variance on aggregated responses because researchers are not confident specifying and interpreting mixed-effects models. This Tutorial explains how to simulate data with random-effects structure and analyze the data using linear mixed-effects regression (with the lme4 R package), with a focus on interpreting the output in light of the simulated parameters. Data simulation not only can enhance understanding of how these models work, but also enables researchers to perform power calculations for complex designs. All materials associated with this article can be accessed at https://osf.io/3cz2e/ .
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A-priori power analysis for a single-predictor multilevel linear regression model using parameters from a previous study indicated that a minimum of 40 participants, each completing 10 pointing task trials, would achieve 83% power.
“Using parameters estimated from own previous study (i.e., fixed effects beta coefficients and random effects’ variance; Kapaj et al., 2023), we found that a minimum of 40 participants, each completing 10 pointing task trials would achieve an 83% power (see data availability statement for study preregistration).”
From The influence of landmark visualization style on task performance, visual attention, and spatial learning in a real-world navigation task (2024) · cites this paper as DeBruine & Barr, 2021
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Pre-verb reactivation of arguments in sentence processing
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Defining daytime in the day-dark approach to measuring the pedestrian reassurance of road lighting
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Simulation-based power analysis could improve the design of clinical trials in Alzheimer’s diseasePreprint
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Computer vision-based animal phenotyping and analysis in presence of uncertain identification
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- Authors
- DeBruine, L. M., & Barr, D. J.
- Affiliations
- University of Glasgow (GB)
- Corresponding author
- DeBruine, Lisa M.
- Venue
- Advances in Methods and Practices in Psychological Science
- Publisher
- SAGE Publications
- Published
- 2021-01
- Volume
- 4
- Issue
- 1
- ISSN
- 2515-2459 (ISSN-L)
- 2515-2467
- OpenAlex
- W2951982695
- Cited by
- 148
- References
- 21
- Citations by year
- 2026: 15 · 2025: 35 · 2024: 34 · 2023: 30 · 2022: 22 · 2021: 11 · 2020: 1
- FWCI
- 18.09
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Advances in Methods and Practices in Psychological Science (publishedVersion, cc-by)
- ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) (acceptedVersion, cc-by-sa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- OSF Preprints (OSF Preprints) (submittedVersion, cc-by-sa)
- Funders
- H2020 European Research Council (647910)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Agriculture, Soil, Plant Science
- Keywords
- mixed models, data simulation, random effects, linear mixed models, lme4, power analysis, experimental design, model interpretation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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