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Using Recursive Partitioning to Account for Parameter Heterogeneity in Multinomial Processing Tree Models

Author

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  • Florian Wickelmaier
  • Achim Zeileis

Abstract

In multinomial processing tree (MPT) models, individual differences between the participants in a study lead to heterogeneity of the model parameters. While subject covariates may explain these differences, it is often unknown in advance how the parameters depend on the available covariates, that is, which variables play a role at all, interact, or have a nonlinear influence, etc. Therefore, a new approach for capturing parameter heterogeneity in MPT models is proposed based on the machine learning method MOB for model-based recursive partitioning. This recursively partitions the covariate space, leading to an MPT tree with subgroups that are directly interpretable in terms of effects and interactions of the covariates. The pros and cons of MPT trees as a means of analyzing the effects of covariates in MPT model parameters are discussed based on a simulation experiment as well as on two empirical applications from memory research. Software that implements MPT trees is provided via the mpttree function in the psychotree package in R.

Suggested Citation

  • 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.
    • Handle: RePEc:inn:wpaper:2016-26
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    References listed on IDEAS

    as
    1. Edgar Merkle & Jinyan Fan & Achim Zeileis, 2014. "Testing for Measurement Invariance with Respect to an Ordinal Variable," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 569-584, October.
    2. 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.
    3. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    4. Carolin Strobl & Julia Kopf & Achim Zeileis, 2015. "Rasch Trees: A New Method for Detecting Differential Item Functioning in the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 289-316, June.
    5. Karl Klauer, 2010. "Hierarchical Multinomial Processing Tree Models: A Latent-Trait Approach," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 70-98, March.
    6. 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.
    7. 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.
    8. Karl Klauer, 2006. "Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 7-31, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    multinomial processing tree; model-based recursive partitioning; parameter heterogeneity;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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