Adjusted priors for Bayes factors involving reparameterized order constraints

DOI:	https://doi.org/10.1016/j.jmp.2016.05.004
URL:	http://arxiv.org/pdf/1511.08775v3.pdf
Weitere URL:	https://www.researchgate.net/profile/Daniel_Heck/p...
Dokumenttyp:	Zeitschriftenartikel
Erscheinungsjahr:	2016
Titel einer Zeitschrift oder einer Reihe:	Journal of Mathematical Psychology
Band/Volume:	73
Seitenbereich:	110-116
Ort der Veröffentlichung:	Amsterdam ; Orlando, FL
Verlag:	Elsevier ; Academic Press
ISSN:	0022-2496
Sprache der Veröffentlichung:	Englisch
Einrichtung:	Fakultät für Sozialwissenschaften > Kognitive Psychologie u. Differentielle Psychologie (Erdfelder 2002-2019) Außerfakultäre Einrichtungen > GESS - CDSS (SOWI)
Fachgebiet:	150 Psychologie
Abstract:	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 image can be reparameterized with auxiliary parameters image to replace the original parameters by image. 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.