Parsimonious Mixed Models

TL;DR

This paper discusses the challenges of fitting mixed-effects models with complex random-effects structures, emphasizing that non-convergence often results from overparameterization rather than estimation issues, and offers diagnostic tools for model simplification.

Contribution

It demonstrates that overparameterization causes convergence problems in mixed models and provides practical diagnostics to identify and simplify complex models.

Findings

Maximal models often fail to converge due to overcomplexity.

Overparameterization can lead to uninterpretable models.

Diagnostic tools can guide effective model simplification.

Abstract

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.