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Keywords
(11)
bayesian approach
bayesian statistics
Beta Distribution
Clinical Assessment
Data Aggregation
Hierarchical Model
Individual Difference
Likelihood Function
Markov Chain Monte Carlo
Statistical Inference
Random Effects
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BetaMPT: Multinomial processing tree models for addressing individual differences
BetaMPT: Multinomial processing tree models for addressing individual differences,10.1016/j.jmp.2009.06.007,Journal of Mathematical Psychology,Jared
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BetaMPT: Multinomial processing tree models for addressing individual differences
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Citations: 2
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Jared B. Smith
,
William H. Batchelder
Traditionally, multinomial processing tree (MPT) models are applied to groups of homogeneous participants, where all participants within a group are assumed to have identical MPT model parameter values. This assumption is unreasonable when MPT models are used for clinical assessment, and it often may be suspect for applications to ordinary psychological experiments. One method for dealing with parameter variability is to incorporate
random effects
assumptions into a model. This is achieved by assuming that participants’ parameters are drawn independently from some specified multivariate hyperdistribution. In this paper we explore the assumption that the hyperdistribution consists of independent beta distributions, one for each MPT model parameter. These betaMPT models are ‘hierarchical models’, and their
statistical inference
is different from the usual approaches based on data aggregated over participants. The paper provides both classical (frequentist) and hierarchical Bayesian approaches to
statistical inference
for betaMPT models. In simple cases the
likelihood function
can be obtained analytically; however, for more complex cases,
Markov Chain Monte Carlo
algorithms are constructed to assist both approaches to inference. Examples based on
clinical assessment
studies are provided to demonstrate the advantages of hierarchical MPT models over aggregate analysis in the presence of individual differences.
Journal:
Journal of Mathematical Psychology  J MATH PSYCHOL
, vol. 54, no. 1, pp. 167183, 2010
DOI:
10.1016/j.jmp.2009.06.007
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