Topics

General literature (helpful for all topics)

Presentation topics

1. Shrinkage

Understanding the concept of shrinkage in multilevel models with practical applications

2. Random-effects structure

Choosing a random-effects structure: Keep it maximal or parsimonious?

  • Bates, D., Kliegl, R., Vasishth, S., & Baayen, H. (2015). Parsimonious mixed models. PDF
  • 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(3), 255-278. PDF
  • Park, J., Cardwell, R., & Yu, H. T. (2020). Specifying the random effect structure in linear mixed effect models for analyzing psycholinguistic data. Methodology, 16(2), 92-111. PDF

3. Model selection and averaging

Different approaches for selecting among multilevel models (Group I)

Model selection for nested and non-nested models. Introduce a selection of criteria such as BIC, Likelihood Ratio Test, R-squared, etc. (but not AIC)

  • Wiley (2020, May 31). Joshua F. Wiley: Linear Mixed Models (LMMs) - Model Comparisons. Retrieved from PDF
  • Cantoni, E., Jacot, N., & Ghisletta, P. (2021). Review and comparison of measures of explained variation and model selection in linear mixed-effects models. Econometrics and Statistics. PDF
  • Müller, S., Scealy, J. L., & Welsh, A. H. (2013). Model selection in linear mixed models. PDF
  • Hamaker, E. L., van Hattum, P., Kuiper, R. M., & Hoijtink, H. (2011). Model selection based on information criteria in multilevel modeling. In J. J. Hox & J. K. Roberts (Eds.), Handbook for advanced multilevel analysis (pp. 231–255)
  • Whittaker, T. A., & Furlow, C. F. (2009). The comparison of model selection criteria when selecting among competing hierarchical linear models. Journal of Modern Applied Statistical Methods, 8(1), 15. PDF
  • Martínez-Huertas JÁ, Olmos R, Ferrer E. Model Selection and Model Averaging for Mixed-Effects Models with Crossed Random Effects for Subjects and Items. Multivariate Behav Res. 2022 Jul-Aug;57(4):603-619. doi: 10.1080/00273171.2021.1889946.

Different approaches for selecting among multilevel models (Group II)

Model selection and model averaging with (conditional) AIC. Introduce AIC and conditional AIC for model selection and model averaging as an alternative to model selection.

  • Sonja Greven, Thomas Kneib, On the behaviour of marginal and conditional AIC in linear mixed models, Biometrika, Volume 97, Issue 4, December 2010, Pages 773–789, https://doi.org/10.1093/biomet/asq042
  • Zhang, X., Zou, G., & Liang, H. (2014). Model averaging and weight choice in linear mixed-effects models. Biometrika, 101(1), 205-218. PDF
  • Säfken, B., Rügamer, D., Kneib, T., & Greven, S. (2021). Conditional Model Selection in Mixed-Effects Models with cAIC4. Journal of Statistical Software, 99(8), 1–30. https://doi.org/10.18637/jss.v099.i08
  • Martínez-Huertas JÁ, Olmos R, Ferrer E. Model Selection and Model Averaging for Mixed-Effects Models with Crossed Random Effects for Subjects and Items. Multivariate Behav Res. 2022 Jul-Aug;57(4):603-619. doi: 10.1080/00273171.2021.1889946.
  • Clark, Michael (2019). Mixed Models with R: Model Comparison. Retrieved from: https://m-clark.github.io/mixed-models-with-R/issues.html#model-comparison
  • R-package cAIC4: Conditional Akaike Information Criterion for ‘lme4’ and ‘nlme’ CRAN

4. Bayesian MLMs

Considerations underlying the choice of prior distributions in Bayesian multilevel models

  • [no presentation]

5. Generalized MLMs

6. Longitudinal Data

Understanding multilevel models for longitudinal data and different covariance matrix specifications of the residual error term

  • West, B. T., Welch, K. B., & Galecki , A. T. (2022). Linear mixed models: a practical guide using statistical software. Crc Press. [Ch. 6,7] (see TU library; E-book)
  • Grace-Martin, K. (NN). The analysis factor. The Unstructured Covariance Matrix: When It Does and Doesn’t Work. Retrieved from: https://www.theanalysisfactor.com/unstructured-covariance-matrix-when-it-does-and-doesn%E2%80%99t-work/
  • Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. Routledge. (see TU library, E-book)
  • Liu, S., Rovine, M. J., & Molenaar, P. (2012). Selecting a linear mixed model for longitudinal data: repeated measures analysis of variance, covariance pattern model, and growth curve approaches. Psychological methods, 17(1), 15. PDF

7. Non-hierarchical models

Understanding non-hierarchical multilevel models: Cross-classified and multiple-membership models.

  • [no presentation]

8. Reporting of Results

Correct and comprehensive reporting of results of a multilevel analysis: Guidelines and helpful tools

  • Huang, F. (2023). Practical multilevel modeling using R. Sage. (Appendix A: Reporting results of multilevel models) PDF
  • Monsalves, M. J., Bangdiwala, A. S., Thabane, A., & Bangdiwala, S. I. (2020). LEVEL (Logical Explanations & Visualizations of Estimates in Linear mixed models): recommendations for reporting multilevel data and analyses. BMC Medical Research Methodology, 20, 1-9. Retrieved from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6945753/
  • Jong, J. (2023) Tools for summarizing and visualizing regression models. Retrieved from: https://cran.r-project.org/web/packages/jtools/vignettes/summ.html
  • Schweinberger, Martin. 2022. Fixed- and Mixed-Effects Regression Models in R. Brisbane: The University of Queensland. url: https://slcladal.github.io/regression.html (Version 2022.09.14).
  • Makowski, D., Lüdecke, D., Patil, I., Thériault, R., Ben-Shachar, M.S., & Wiernik, B.M. (2023). Automated Results Reporting as a Practical Tool to Improve Reproducibility and Methodological Best Practices Adoption. CRAN. Available from https://easystats.github.io/report/
  • Brown, V. A. (2021). An introduction to linear mixed-effects modeling in R. Advances in Methods and Practices in Psychological Science, 4(1), Retrieved from: https://journals.sagepub.com/doi/10.1177/2515245920960351

9. Big Data

Multilevel models for big data: Approaches for handling very large data sets

  • Verbeke, G., Molenberghs, G., Fieuws, S., Iddi, S. (2018). Mixed Models with Emphasis on Large Data Sets. In: Speelman, D., Heylen, K., Geeraerts, D. (eds) Mixed-Effects Regression Models in Linguistics. Quantitative Methods in the Humanities and Social Sciences. Springer, Cham. Retrieved from: https://link.springer.com/chapter/10.1007/978-3-319-69830-4_2
  • Clark, Michael (2019). Mixed Models for Big Data. Retrieved from: https://m-clark.github.io/posts/2019-10-20-big-mixed-models/
  • Lee, J. Y., Brown, J. J., & Ryan, L. M. (2017). Sufficiency revisited: Rethinking statistical algorithms in the big data era. The American Statistician, 71(3), 202-208.