IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i1p205-235.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9374-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9374-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. repec:cup:judgdm:v:6:y:2011:i:8:p:832-842 is not listed on IDEAS
    4. Karl Klauer, 2010. "Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 70-98, March.
    5. 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.
    6. Karl Klauer, 2006. "Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 7-31, March.
    7. Paul Boeck, 2008. "Random Item IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 533-559, December.
    8. 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).
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. repec:cup:judgdm:v:12:y:2017:i:6:p:537-552 is not listed on IDEAS
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Zita Oravecz & Royce Anders & William Batchelder, 2015. "Hierarchical Bayesian Modeling for Test Theory Without an Answer Key," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 341-364, June.
    4. 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.
    5. Royce Anders & William Batchelder, 2015. "Cultural Consensus Theory for the Ordinal Data Case," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 151-181, March.
    6. 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.
    7. T. Loeys & Y. Rosseel & K. Baten, 2011. "A Joint Modeling Approach for Reaction Time and Accuracy in Psycholinguistic Experiments," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 487-503, July.
    8. 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.
    9. Quinn N. Lathrop & Ying Cheng, 2017. "Item Cloning Variation and the Impact on the Parameters of Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 245-263, March.
    10. Nana Kim & Daniel M. Bolt & James Wollack, 2022. "Noncompensatory MIRT For Passage-Based Tests," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 992-1009, September.
    11. repec:cup:judgdm:v:12:y:2017:i:6:p:537-552 is not listed on IDEAS
    12. Andrés López-Sepulcre & Sebastiano De Bona & Janne K. Valkonen & Kate D.L. Umbers & Johanna Mappes, 2015. "Item Response Trees: a recommended method for analyzing categorical data in behavioral studies," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(5), pages 1268-1273.
    13. Antonio Caronni & Marina Ramella & Pietro Arcuri & Claudia Salatino & Lucia Pigini & Maurizio Saruggia & Chiara Folini & Stefano Scarano & Rosa Maria Converti, 2023. "The Rasch Analysis Shows Poor Construct Validity and Low Reliability of the Quebec User Evaluation of Satisfaction with Assistive Technology 2.0 (QUEST 2.0) Questionnaire," IJERPH, MDPI, vol. 20(2), pages 1-19, January.
    14. Sun-Joo Cho & Allan S. Cohen, 2010. "A Multilevel Mixture IRT Model With an Application to DIF," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 336-370, June.
    15. Lauren E. Montgomery & Michael D. Lee, 2021. "Expert and novice sensitivity to environmental regularities in predicting NFL games," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1370-1391, November.
    16. Edgar C. Merkle & Daniel Furr & Sophia Rabe-Hesketh, 2019. "Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 802-829, September.
    17. Sun-Joo Cho & Sarah Brown-Schmidt & Woo-yeol Lee, 2018. "Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 751-771, September.
    18. Sijia Huang & Li Cai, 2024. "Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 311-341, June.
    19. Mariagiulia Matteucci & Bernard Veldkamp, 2015. "The approach of power priors for ability estimation in IRT models," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 917-926, May.
    20. Mark Steyvers & Thomas S. Wallsten & Edgar C. Merkle & Brandon M. Turner, 2014. "Evaluating Probabilistic Forecasts with Bayesian Signal Detection Models," Risk Analysis, John Wiley & Sons, vol. 34(3), pages 435-452, March.
    21. Paul Boeck & Sun-Joo Cho, 2021. "Not all DIF is shaped similarly," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 712-716, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:205-235. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.