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Benefits of response time-extended multinomial processing tree models: A reply to Starns (2018)


In his comment on Heck and Erdfelder (2016, Psychonomic Bulletin & Review, 23, 1440–1465), Starns (2018, Psychonomic Bulletin & Review, 25, 2406–2416) focuses on the response time-extended two-high-threshold (2HT-RT) model for yes-no recognition tasks, a specific example for the general class of response time-extended multinomial processing tree models (MPT-RTs) we proposed. He argues that the 2HT-RT model cannot accommodate the speed–accuracy trade-off, a key mechanism in speeded recognition tasks. As a remedy, he proposes a specific discrete-state model for recognition memory that assumes a race mechanism for detection and guessing. In this reply, we clarify our motivation for using the 2HT-RT model as an example and highlight the importance and benefits of MPT-RTs as a flexible class of general-purpose, simple-to-use models. By binning RTs into discrete categories, the MPT-RT approach facilitates the joint modeling of discrete responses and response times in a variety of psychological paradigms. In fact, many paradigms either lack a clear-cut accuracy criterion or show performance levels at ceiling, making corrections for incautious responding redundant. Moreover, we show that some forms of speed–accuracy trade-off can in fact not only be accommodated but also be measured by appropriately designed MPT-RTs.

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  1. 1.

    Here, we refer to the race model as a “process model” because it assumes a specific processing mechanism to account for speed–accuracy trade-offs (i.e., a latent race). However, some formal theorists may prefer the label “measurement model”.

  2. 2.

    In Starns’ comment, this issue is briefly discussed in the section “Differences in guessing RTs”.

  3. 3.

    Obviously, technical complexity itself is not a drawback. In an ideal world, if a technically complex model turns out to be necessary to explain a cognitive phenomenon, researchers should improve their skills instead of falling back to simple methods.

  4. 4.

    We thank David Kellen for outlining this important point very clearly.

  5. 5.

    Note that Brainerd et al., (2019) refer to guessing processes as bias processes.


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We thank Jeff Starns, David Kellen, and an anonymous reviewer for helpful and constructive comments on an earlier version of the manuscript. R code for the simulations is available at the Open Science Framework at https://osf.io/qkfxz/. This work was supported by the research training group Statistical Modeling in Psychology, funded by the German Research Foundation (DFG; grant GRK 2277).

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Correspondence to Daniel W. Heck.

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Heck, D.W., Erdfelder, E. Benefits of response time-extended multinomial processing tree models: A reply to Starns (2018). Psychon Bull Rev (2020). https://doi.org/10.3758/s13423-019-01663-0

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  • MPT model
  • Processing speed
  • Reaction time
  • Discrete-state models
  • Speed–accuracy trade-off