Frontiers in Psychology (Jun 2014)
Using a Multinomial Tree Model for Detecting Mixtures in Perceptual Detection
Abstract
In the area of memory research there have been two rival approaches for memory measurement– signal detection theory (SDT) and multinomial processing trees (MPT). Both approaches provide measures for the quality of the memory representation, and both approaches provide for corrections for response bias. In recent years there has been a strongcase advanced for the MPT approach because of the finding of stochastic mixtures on both target-present and target-absent tests. In this paper a case is made that perceptual detection, like memory recognition, involves a mixture of processes that are more readily modeled by a MPT model. The Chechile (2004) 6P memory measurement model is modified in order to apply to the case of perceptual detection; this new MPT model is called the Perceptual Detection (PD) model. The properties of the PD model are developed, and the model is applied to some existing data of a radiologist examining CT scans. The PD model brings out novel features that were absent from a standard SDT analysis. Also the topic of optimal parameter estimation on an individual-observer basis is explored with Monte Carlo simulations. Thesesimulations reveal that the mean of the Bayesian posterior distribution is a more accurate estimator than the corresponding maximum likelihood estimator (MLE). Monte Carlo simulations also indicate that model estimates based on only the data from an individual observer can be improved upon (in the sense of being more accurate) by an adjustment that makes the mean estimate for a group of individuals equal to the estimate based on the data pooledacross all the observers. This result is discussed as an analogous statistical finding to the improvements over the MLE demonstrated by the James-Stein shrinkage estimator in the case of the linear, multi-group normal model.
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