An introduction to Bayesian hierarchical models with an application in the theory of signal detection |
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Authors: | Email author" target="_blank">Jeffrey?N?RouderEmail author Jun?Lu |
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Institution: | Department of Psychological Sciences, 210 McAlester Hall, University of Missouri, Columbia, MO 65211, USA. rouderj@missouri.edu |
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Abstract: | Although many nonlinear models of cognition have been proposed in the past 50 years, there has been little consideration of
corresponding statistical techniques for their analysis. In analyses with nonlinear models, unmodeled variability from the
selection of items or participants may lead to asymptotically biased estimation. This asymptotic bias, in turn, renders inference
problematic. We show, for example, that a signal detection analysis of recognition memory data leads to asymptotic underestimation
of sensitivity. To eliminate asymptotic bias, we advocate hierarchical models in which participant variability, item variability,
and measurement error are modeled simultaneously. By accounting for multiple sources of variability, hierarchical models yield
consistent and accurate estimates of participant and item effects in recognition memory. This article is written in tutorial
format; we provide an introduction to Bayesian statistics, hierarchical modeling, and Markov chain Monte Carlo computational
techniques. |
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Keywords: | |
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