We highlight the importance of adjusting the prior distribution of a reparameterized model when computing the Bayes factor for model selection. Specifically, we derive adjusted priors for linear order constraints in multinomial processing tree (MPT) models, which are often reparameterized by scaling parameters.
As an example, the order constraint on the probabilities $\theta_1 \leq \theta_2$ is equivalent to the reparameterization $\eta_2=\theta_2$, $\eta_1=\theta_1/\theta_2$. Intuitively, the parameter $\eta_1$ measures the amount of shrinkage between the two orginal parameters.
This repository contains:
* a detailed comparison of the product-binomial model (see main paper) with respect to parameter estimates, marginal probabilities, and the Bayes factor
* details about the importance sampler used to compute the marginal probability for the pair-clustering model (including R code and results for Experiment 1 and 4 of Riefer et al., 2002)
