Below are some recommended readings and other resources for mixed-effects models, both in factorial designs and for truly longitudinal models.

  1. Long, J. D. (2012). Longitudinal data analysis for the behavioral sciences using R. Sage.

  2. Singer, J. D., Willett, J. B., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford university press.

  3. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (Vol. 1). Sage.

  4. Garcia, T. P., & Marder, K. (2017). Statistical approaches to longitudinal data analysis in neurodegenerative diseases: Huntington’s disease as a model. Current Neurology and Neuroscience Reports, 17(2), 14.

  5. Lohse, K. R., Shen, J., & Kozlowski, A. J. (2020). Modeling longitudinal outcomes: A contrast of two methods. Journal of Motor Learning and Development, 8(1), 145-165.

  6. Dr. Daniel Wollschläger has a great online reference for mixed-effect models in different factorial designs: http://www.dwoll.de/rexrepos/posts/anovaMixed.html

  7. This book is definitely a bit more dense, but is a fantastic resource for both linear and nonlinear mixed models: Pinheiro, J., & Bates, D. (2006). Mixed-effects models in S and S-PLUS. Springer Science & Business Media.

  8. And, as always, the lme4 manual is super important to read if your haven’t already: Bates, D., Mächler, M., Bolker, B., & Walker, S. (2014). Fitting linear mixed-effects models using lme4. arXiv preprint arXiv:1406.5823.

  9. Kuznetsova, A., Brockhoff, P. B., & Christensen, R. H. (2017). lmerTest package: tests in linear mixed effects models. Journal of statistical software, 82(13), 1-26.

  10. Josh Errickson also has a nice visualization of crossed versus nested variables and how they can be represented as random-effects: https://errickson.net/stats-notes/vizrandomeffects.html

  11. Dr. Violet Brown has a great didactic paper on mixed-effects models in psycholinguistics, where both stimuli and subjects are treated as random samples (requiring a doubling of the random-effects stucture when specifying your models): https://journals.sagepub.com/doi/full/10.1177/2515245920960351