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Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables

Abstract

Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.

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Correspondence to Daniel W. Heck.

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This research was supported by the research training group Statistical Modeling in Psychology (GRK 2277), funded by the German Research Foundation (DFG), and the University of Mannheim’s Graduate School of Economic and Social Sciences (GSC 26), also funded by the DFG. All data and R scripts for the simulations and the empirical analysis are available in the supplementary material at https://osf.io/fyeum.

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Heck, D.W., Erdfelder, E. & Kieslich, P.J. Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables. Psychometrika 83, 893–918 (2018). https://doi.org/10.1007/s11336-018-9622-0

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Keywords

  • multinomial processing tree model
  • discrete states
  • mixture model
  • cognitive modeling
  • response times
  • mouse-tracking