  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.
