  Multinomial processing tree (MPT) models are tools for disentangling the
contributions of latent cognitive processes in a given experimental paradigm.
The present note analyzes MPT models subject to order constraints on subsets of
its parameters. The constraints that we consider frequently arise in cases
where the response categories are ordered in some sense such as in
confidence-rating data, Likert scale data, where graded guessing tendencies or
response biases are created via base-rate or payoff manipulations, in the
analysis of contingency tables with order constraints, and in many other cases.
We show how to construct an MPT model without order constraints that is
statistically equivalent to the MPT model with order constraints. This new
closure result extends the mathematical analysis of the MPT class, and it
offers an approach to order-restricted inference that extends the approaches
discussed by Knapp and Batchelder (2004). The usefulness of the method is
illustrated by means of an analysis of an order-constrained version of the
two-high-threshold model for confidence ratings.
