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04-04-2019 | Original Article

Are model parameters linked to processing stages? An empirical investigation for the ex-Gaussian, ex-Wald, and EZ diffusion models

Auteurs: Tobias Rieger, Jeff Miller

Gepubliceerd in: Psychological Research | Uitgave 6/2020

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Abstract

In previous research, the parameters of the ex-Gaussian distribution have been subject to a wide variety of interpretations. The present study investigated whether the ex-Gaussian model is capable of distinguishing effects on separate processing stages (i.e., pre-motor vs. motor). In order to do so, we used datasets where the locus of effect was quite clear. Specifically, we analyzed data from experiments comparing hand vs. foot responses—presumably differing in the motor stage—and from experiments in which the lateralized readiness potential was used to localize experimental effects into premotor vs. motor processes. Moreover, we broadened the scope to two other descriptive RT models: the ex-Wald and EZ diffusion models. To the extent possible with each of these models, we reanalyzed the RT data of 19 clearly localized experimental effects from 12 separate experiments reported in seven previously published articles. Unfortunately, we did not find a clear pattern of results for any of the models, with no clear link between effects on one of the model’s parameters and effects on different processing stages. The present results suggest that one should resist the temptation to associate specific processing stages with individual parameters of the ex-Gaussian, ex-Wald, and EZ diffusion models.
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Voetnoten
1
Schwarz (2001) interprets the diffusion process as an accumulation of noisy partial information over time. Thus, the ex-Wald model has one additional noise parameter which is just an arbitrary scaling parameter usually set to one for the parameter estimations. See Schwarz (2001) for further methodological and mathematical details.
 
2
For the mathematical derivation of the EZ diffusion model and more details about prerequisites, assumptions, and parameter recovery, see Wagenmakers et al. (2007).
 
3
Comparisons of EZ diffusion model parameters were not possible for the experiments from Miller and Ulrich (1998), Miller and Low (2001), or Miller (2012), because those experiments used simple, go/no-go, 4-choice, and 6-choice tasks, whereas the EZ diffusion model is only applicable to 2-choice tasks.
 
4
The average numbers of trials per cell reported in Tables 1 and 2 exclude error trials, so they are slight underestimates of the numbers of trials used for parameter estimation for the EZ diffusion model.
 
5
We also ran a parallel set of analyses including participants who were excluded from the published analyses due to issues with EEG recording, and these analyses produced very similar results.
 
6
We also separately checked the results for the drift rate v and the boundary separation a and found that the effects on TD were mostly driven by v. These detailed results can be found in the online supplement.
 
7
We also checked whether parameters of the shifted Wald (Heathcote, 2004)—where the non-Wald parameter is a constant shift rather than an exponential—can be linked to processing stages. Though the results across the hand vs. foot experiments were rather consistent, there was no clear pattern of results for the LRP experiments. For details see the online supplement.
 
8
We also fitted the EZ2 diffusion model (Grasman, Wagenmakers, & van der Maas, 2009)—an extension to the EZ diffusion model that allows for variations in starting point z—to the same datasets as the EZ diffusion model. However, the obtained pattern of results was no more systematic regarding effects on different stages than the result pattern produced by the EZ diffusion model, so we did not include it.
 
Literatuur
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Metagegevens
Titel
Are model parameters linked to processing stages? An empirical investigation for the ex-Gaussian, ex-Wald, and EZ diffusion models
Auteurs
Tobias Rieger
Jeff Miller
Publicatiedatum
04-04-2019
Uitgeverij
Springer Berlin Heidelberg
Gepubliceerd in
Psychological Research / Uitgave 6/2020
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI
https://doi.org/10.1007/s00426-019-01176-4

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