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A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population
Abstract
This article investigates the impact of the normality assumption for random effects on their estimates in the linear mixed-effects model. It shows that if the distribution of random effects is a finite mixture of normal distributions, then the random effects may be badly estimated if normality is assumed, and the current methods for inspecting the appropriateness of the model assumptions are not sound. Further, it is argued that a better way to detect the components of the mixture is to build this assumption in the model and then “compare” the fitted model with the Gaussian model. All of this is illustrated on two practical examples.
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Citations
Cited by
Robustness of linear mixed-effects models to violations of distributional assumptions
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) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.13434 · Cited by 1,393
“Unfortunately, very few studies have assessed random effect variances and predictions (e.g. Maas & Hox, 2004; McCulloch & Neuhaus, 2011; Verbeke & Lesaffre, 1996); for those who did, the estimation of the group variance is usually accurate, but random effect coefficients (best linear unbiased…”
BackgroundMethodExperience sampling methodology in mental health research: new insights and technical developments.
Myin‐Germeys, I., Kasanova, Z., Vaessen, T., Vachon, H., Kirtley, O., Viechtbauer, W., & Reininghaus, U. (2018) · World Psychiatry · doi:10.1002/wps.20513 · Cited by 709
Bauer, D. J., & Curran, P. J. (2004) · Psychological Methods · doi:10.1037/1082-989x.9.1.3 · Cited by 536
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Myers, R. A., Bowen, K. G., & Barrowman, N. J. (1999) · Canadian Journal of Fisheries and Aquatic Sciences · doi:10.1139/f99-201 · Cited by 503
Brown, C. H., Wang, W., Kellam, S. G., Muthén, B. O., Petras, H., Toyinbo, P., Poduska, J., Ialongo, N., Wyman, P. A., Chamberlain, P., et al. (2008) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2007.11.013 · Cited by 177
Metadata
- Authors
- Verbeke, G., & Lesaffre, E.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1996-03
- Volume
- 91
- Issue
- 433
- Pages
- 217-221
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2059166063
- Cited by
- 594
- References
- 0
- FWCI
- 5.94
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population. https://app.cochat.ai/papers/10.1080/01621459.1996.10476679
- The paper
- Verbeke, G., & Lesaffre, E. (1996). A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1996.10476679
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
