  Many psychological theories that are instantiated as statistical models imply
order constraints on the model parameters. To fit and test such restrictions,
order constraints of the form $\theta_i \leq \theta_j$ can be reparameterized
with auxiliary parameters $\eta\in [0,1]$ to replace the original parameters by
$\theta_i = \eta\cdot\theta_j$. This approach is especially common in
multinomial processing tree (MPT) modeling because the reparameterized, less
complex model also belongs to the MPT class. Here, we discuss the importance of
adjusting the prior distributions for the auxiliary parameters of a
reparameterized model. This adjustment is important for computing the Bayes
factor, a model selection criterion that measures the evidence in favor of an
order constraint by trading off model fit and complexity. We show that uniform
priors for the auxiliary parameters result in a Bayes factor that differs from
the one that is obtained using a multivariate uniform prior on the
order-constrained original parameters. As a remedy, we derive the adjusted
priors for the auxiliary parameters of the reparameterized model. The practical
relevance of the problem is underscored with a concrete example using the
multi-trial pair-clustering model.
