RT-MPTs: Multinomial processing tree models and response latencies
Final Report Abstract
The goal of the project is to bring together two strong strands of psychological research bent on analyzing mental processes: the mathematical modeling of response time distributions and multinomial processing tree models (MPT models). MPT models are models for categorical data that are tailored to a specific experimental paradigm. They have been found useful in many research domains in psychology. The family of MPT models is to be extended in the project such that responses and response latencies can be modeled simultaneously allowing one to estimate distributions of completion times of those mental processes considered in the underlying MPT model. This goal is to be realized with different distributional assumptions. A first implementation assumes that process completion times are exponentially distributed. The model is implemented hierarchically so that not only mean tendencies but also individual differences can be modeled. The algorithm for fitting the resulting model has been validated by recovery studies as well as by the method of simulation-based calibration. It has been applied on data from recognition memory. It has been extended in different ways and is available as a user-friendly R package.. For several reasons it is desirable to develop similar models with alternative assumptions for the distribution of process completion times. Having several such options allow one, for example, to assess the robustness of inferences emerging form the model analyses against specific distributional assumptions. The assumption of exponential process completion times has moreover been criticized on substantive psychological grounds. A second implementation assumes, for such reasons, that process completion times and the probabilities of different process outcomes of each process follow a diffusion model. This assumption is psychologically more plausible and leads to more realistic predicted distributions of process completion times, but is mathematically more demanding. Developing the model with diffusion-model kernel required preparatory work on the derivatives of the densities of first-passage time distributions under the diffusion model and an efficient algorithm for generating samples from such distributions. Based on this foundation, an algorithm for fitting the resulting model with diffusion-model kernel could be successfully constructed. Like the algorithm for the model with exponential distributions of process completion times, we validated the resulting hierarchical algorithm via recovery studies and by means of simulation-based validation. We applied the algorithm to the same corpus of data as for the model with exponentially distributed processcompletion times and included it in our R package. The new method provides an extension of traditional diffusion model analyses where a multinomial model has been proposed for the modeled paradigm. Both the exponential and the diffusion-model versions of our method can be applied to any MPT model and allow one to estimate process completion times and process-outcome probabilities, and to test hypotheses about them as well as about the processing architecture.
Publications
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RT-MPTs: Process models for response-time distributions based on multinomial processing trees with applications to recognition memory. Journal of Mathematical Psychology, 82, 111-130.
Klauer, Karl Christoph & Kellen, David
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Extending RT-MPTs to enable equal process times. Journal of Mathematical Psychology, 96, 102340.
Hartmann, Raphael & Klauer, Karl Christoph
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rtmpt: An R package for fitting response-time extended multinomial processing tree models. Behavior Research Methods, 52(3), 1313-1338.
Hartmann, Raphael; Johannsen, Lea & Klauer, Karl Christoph
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Partial derivatives for the first-passage time distribution in Wiener diffusion models. Journal of Mathematical Psychology, 103, 102550.
Hartmann, Raphael & Klauer, Karl Christoph
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An adaptive rejection sampler for sampling from the Wiener diffusion model. Behavior Research Methods, 55(5), 2283-2296.
Hartmann, Raphael; Meyer-Grant, Constantin G. & Klauer, Karl Christoph
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The Seven-parameter Diffusion Model: an Implementation in Stan for Bayesian Analyses. Behavior Research Methods, 56(4), 3102-3116.
Henrich, Franziska; Hartmann, Raphael; Pratz, Valentin; Voss, Andreas & Klauer, Karl Christoph
