How to Set Priors for Hypothesis Testing in Generalized Linear Models: A Three-Step Workflow with an Application to Binomial Models

Researchers using Bayesian hypothesis testing in binomial generalized linear models (GLMs) - for instance, logistic regression for accuracy data - need priors on regression coefficients, but no principled framework exists for choosing them. The nonlinear link function creates a prior-link interaction: priors that appear reasonable on the coefficient scale can imply implausible distributions on the probability scale. We show that this problem has an elegant solution for cumulative-distribution-function (CDF) based link functions: matched priors - prior families that mirror the link function - produce exactly uniform distributions on the probability scale, providing a maximally uninformative anchor. For logistic regression, the matched Logistic(0, 0.75) intercept prior and Logistic(0, 0.25–0.30) effect prior provide well-calibrated Bayes Factors across a wide range of experimental scenarios. We embed this matched-prior principle in a three-step workflow - (1) identify matched priors, (2) evaluate prior predictive distributions, (3) calibrate Bayes Factors - and demonstrate it fully for binomial GLMs with ready-to-use brms code. Scaling formulas allow researchers to adapt the defaults to any contrast coding, predictor scale, or informed prior belief. The workflow transfers directly to ordinal, lognormal, count, beta, and distributional regression models.