Bayesian hierarchical models for the recognition-memory experiments
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Bayesian hierarchical probit models are developed for analyzing the data from the recognition-memory experiment in Psychology. Both informative priors and non-informative priors are investigated. For the informative priors, two latent variable structure priors are proposed. One is a generalization of the share-component prior in Lu et al. (2007). The other uses a structure from factor analysis. The latent variable structure priors model the correlation across participant effects and item effects flexibly by not requiring the predetermination of the correlation sign. Meanwhile, three options for objective Bayesian analysis are developed. One option is to use shrinkage priors by assigning bivariate normal priors on participant effect parameters and item effect parameters at the first level, and objective priors such as a constant prior on the covariance matrices. The second option is to assign the constant prior for all of the effect parameters. The third option is to apply the constant prior to the two overall mean effects and hierarchical priors to the participant and item effects with a class of non-informative priors on the variance components. The conditions for the propriety of posteriors are examined under different non-informative priors. Simulation studies and real data analyses are conducted for comparing proposed and some existing methods.
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