Parsimonious Mixed Models

By Douglas M. Bates, Reinhold Kliegl, Shravan Vasishth, Harald Baayen. 2015

1,508 citations recorded by the source corpus.

The analysis of experimental data with mixed-effects models requires decisions about the specification of the appropriate random-effects structure. Recently, Barr, Levy, Scheepers, and Tily, 2013 recommended fitting `maximal' models with all possible random effect components included. Estimation of maximal models, however, may not converge. We show that failure to converge typically is not due to a suboptimal estimation algorithm, but is a consequence of attempting to fit a model that is too complex to be properly supported by the data, irrespective of whether estimation is based on maximum likelihood or on Bayesian hierarchical modeling with uninformative or weakly informative priors. Importantly, even under convergence, overparameterization may lead to uninterpretable models. We provide diagnostic tools for detecting overparameterization and guiding model simplification.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3ec198a8e383f9e0541ace670452dee52f1eb1d3

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Citations in the corpus

Estimating power in (generalized) linear mixed models: An open introduction and tutorial in R (2020, background): “This paper is designed to meet the needs of researchers who have some experience with mixed-effects modeling, and thus does not discuss topics such as model selection or optimal random-effects structure (Barr, Levy, Scheepers, & Tily, 2013; Bates, Kliegl, Vasishth, & Baayen, 2015a).”
Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS (2017, background): “In this case, the term could perhaps be discarded to avoid overparametrization (Bates et al., 2015).”
A brief introduction to mixed effects modelling and multi-model inference in ecology (2018, methodology): “…notation equivalent to fitting the proposed models in the statistical software R (R Core Team 2016), with the LMMs fitted using the R package lme4 (Bates et al. 2015): Fitting ‘group’ as a fixed effect in model M1 assumes the 5 ‘group’ means are all independent of one another, and share a common…”
Repeated Measures Correlation (2017, background): “Overfitting may produce uninterpretable results, so model comparison is essential (Singer and Willett, 2003; Bates et al., 2015).”
A meta-analysis of syntactic priming in language production (2016, methodology): “Following Bates et al. (2015) and using the RePsychLing package, we first fit the maximal justified model and then simplified it to obtain convergence and avoid overparameterization.”
Mixed Effects Models are Sometimes Terrible (2017, methodology): “As Bates et al. (2015b) discussed, this is not a typical design.”
The cave of Shadows. Addressing the human factor with generalized additive mixed models (2015, methodology): “Addressing the autocorrelation issue for the KKL data set does not lead to major changes in significances and magnitudes of fixed-effect coefficients and the magnitudes of the (significant) coefficients, as reported in Bates et al. (2015) and Kliegl et al. (2015).”
Balancing Type I Error and Power in Linear Mixed Models (2015, background): “There are also some specific proposals for selection of parsimonious mixed models (e.g., Bates et al., 2015a).”