Balancing Type I Error and Power in Linear Mixed Models

TL;DR

This paper examines the trade-off between Type I error and statistical power in linear mixed models, proposing model selection over maximal models to optimize inference in psycholinguistic research.

Contribution

It introduces a data-driven model selection approach to balance Type I error and power in linear mixed-effects models, improving inference accuracy.

Findings

Maximal models can reduce power despite controlling Type I error.

Model selection based on data supports better power without increasing Type I error.

Simulations demonstrate advantages of model selection over maximal models.

Abstract

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 et al. 2013), presumably to keep Type I error down to the nominal alpha 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.