Bayes factors for logistic (mixed effect) models

In psychology, we often want to know whether or not an effect exists. The traditional way of answering this question is to use frequentist statistics. However, a significance test against a null hypothesis of no effect cannot distinguish between two states of affairs: evidence of absence of an effect, and absence of evidence for or against an effect. Bayes factors can make this distinction; however, uptake of Bayes factors in psychology has so far been low for two reasons. Firstly, they require researchers to specify the range of effect sizes their theory predicts. Researchers are often unsure about how to do this, leading to the use of inappropriate default values which may give misleading results. Secondly, many implementations of Bayes factors have a substantial technical learning curve. We present a case study and simulations demonstrating a simple method for generating a range of plausible effect sizes, i.e. a model of H1, for treatment effects where there is a binary dependent variable. We illustrate this using mainly the estimates from frequentist logistic mixed-effects models (because of their widespread adoption), but also using Bayesian model comparison with Bayesian hierarchical models (which have increased flexibility). Bayes factors calculated using these estimates provide intuitively reasonable results across a range of real effect sizes.