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

Parametric Order Constraints in Multinomial Processing Tree Models: An Extension of Knapp and Batchelder (2004)