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Bayesian Estimation of Multinomial Processing Tree Models with Heterogeneity in Participants and Items

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  • Dora Matzke
  • Conor Dolan
  • William Batchelder
  • Eric-Jan Wagenmakers

Abstract

Multinomial processing tree (MPT) models are theoretically motivated stochastic models for the analysis of categorical data. Here we focus on a crossed-random effects extension of the Bayesian latent-trait pair-clustering MPT model. Our approach assumes that participant and item effects combine additively on the probit scale and postulates (multivariate) normal distributions for the random effects. We provide a WinBUGS implementation of the crossed-random effects pair-clustering model and an application to novel experimental data. The present approach may be adapted to handle other MPT models. Copyright The Psychometric Society 2015

Suggested Citation

  • Dora Matzke & Conor Dolan & William Batchelder & Eric-Jan Wagenmakers, 2015. "Bayesian Estimation of Multinomial Processing Tree Models with Heterogeneity in Participants and Items," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 205-235, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:205-235
    DOI: 10.1007/s11336-013-9374-9
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    References listed on IDEAS

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    1. repec:cup:judgdm:v:6:y:2011:i:8:p:832-842 is not listed on IDEAS
    2. De Boeck, Paul & Partchev, Ivailo, 2012. "IRTrees: Tree-Based Item Response Models of the GLMM Family," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(c01).
    3. Jeffrey Rouder & Dongchu Sun & Paul Speckman & Jun Lu & Duo Zhou, 2003. "A hierarchical bayesian statistical framework for response time distributions," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 589-606, December.
    4. George Karabatsos & William Batchelder, 2003. "Markov chain estimation for test theory without an answer key," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 373-389, September.
    5. Karl Klauer, 2006. "Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 7-31, March.
    6. Jeffrey Rouder & Jun Lu & Dongchu Sun & Paul Speckman & Richard Morey & Moshe Naveh-Benjamin, 2007. "Signal Detection Models with Random Participant and Item Effects," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 621-642, December.
    7. Xiangen Hu & William Batchelder, 1994. "The statistical analysis of general processing tree models with the EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 21-47, March.
    8. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    9. Karl Klauer, 2010. "Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 70-98, March.
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    Cited by:

    1. repec:cup:judgdm:v:12:y:2017:i:6:p:537-552 is not listed on IDEAS
    2. Marta Castela & Edgar Erdfelder, 2017. "Further evidence for the memory state heuristic: Recognition latency predictions for binary inferences," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 12(6), pages 537-552, November.
    3. Quentin F. Gronau & Eric-Jan Wagenmakers & Daniel W. Heck & Dora Matzke, 2019. "A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree Models Using Warp-III Bridge Sampling," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 261-284, March.
    4. Florian Wickelmaier & Achim Zeileis, 2016. "Using Recursive Partitioning to Account for Parameter Heterogeneity in Multinomial Processing Tree Models," Working Papers 2016-26, Faculty of Economics and Statistics, Universität Innsbruck.
    5. Sun-Joo Cho & Sarah Brown-Schmidt & Paul De Boeck & Jianhong Shen, 2020. "Modeling Intensive Polytomous Time-Series Eye-Tracking Data: A Dynamic Tree-Based Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 154-184, March.
    6. Daniel W. Heck & Edgar Erdfelder & Pascal J. Kieslich, 2018. "Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 893-918, December.
    7. Steffen Nestler & Edgar Erdfelder, 2023. "Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 809-829, September.

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