Balancing Type I error and power in linear mixed models

- We show that “Keeping it maximal” comes with a cost for LMMs.
- Maximal models may lose power if their complexity is not supported by the data.
- Model selection can balance Type-I error rates with power.

Linear mixed-effects models have increasingly replaced mixed-model analyses of variance for statistical inference in factorial psycholinguistic experiments. Although LMMs have many advantages over ANOVA, like ANOVAs, setting them up for data analysis also requires some care. One simple option, when numerically possible, is to fit the full variance-covariance structure of random effects (the maximal model; Barr, Levy, Scheepers & Tily, 2013), presumably to keep Type I error down to the nominal α in the presence of random effects. Although it is true that fitting a model with only random intercepts may lead to higher Type I error, fitting a maximal model also has a cost: it can lead to a significant loss of power. We demonstrate this with simulations and suggest that for typical psychological and psycholinguistic data, higher power is achieved without inflating Type I error rate if a model selection criterion is used to select a random effect structure that is supported by the data.