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The Lognormal Race: A Cognitive-Process Model of Choice and Latency with Desirable Psychometric Properties

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  • Jeffrey Rouder
  • Jordan Province
  • Richard Morey
  • Pablo Gomez
  • Andrew Heathcote

Abstract

We present a cognitive process model of response choice and response time performance data that has excellent psychometric properties and may be used in a wide variety of contexts. In the model there is an accumulator associated with each response option. These accumulators have bounds, and the first accumulator to reach its bound determines the response time and response choice. The times at which accumulator reaches its bound is assumed to be lognormally distributed, hence the model is race or minima process among lognormal variables. A key property of the model is that it is relatively straightforward to place a wide variety of models on the logarithm of these finishing times including linear models, structural equation models, autoregressive models, growth-curve models, etc. Consequently, the model has excellent statistical and psychometric properties and can be used in a wide range of contexts, from laboratory experiments to high-stakes testing, to assess performance. We provide a Bayesian hierarchical analysis of the model, and illustrate its flexibility with an application in testing and one in lexical decision making, a reading skill. Copyright The Psychometric Society 2015

Suggested Citation

  • Jeffrey Rouder & Jordan Province & Richard Morey & Pablo Gomez & Andrew Heathcote, 2015. "The Lognormal Race: A Cognitive-Process Model of Choice and Latency with Desirable Psychometric Properties," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 491-513, June.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:491-513
    DOI: 10.1007/s11336-013-9396-3
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    References listed on IDEAS

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    1. Wim van der Linden, 2007. "A Hierarchical Framework for Modeling Speed and Accuracy on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 287-308, September.
    2. P. Wild & W. R. Gilks, 1993. "Adaptive Rejection Sampling from Log‐Concave Density Functions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(4), pages 701-709, December.
    3. Jeffrey Rouder, 2005. "Are unshifted distributional models appropriate for response time?," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 377-381, June.
    4. Jeffrey Rouder & Dongchu Sun & Paul Speckman & Jun Lu & Duo Zhou, 2003. "A hierarchical bayesian statistical framework for response time distributions," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 589-606, December.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Peter Craigmile & Mario Peruggia & Trisha Van Zandt, 2010. "Hierarchical Bayes Models for Response Time Data," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 613-632, December.
    7. Gerard Breukelen, 2005. "Psychometric Modeling of response speed and accuracy with mixed and conditional regression," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 359-376, June.
    8. G. O. Roberts & S. K. Sahu, 1997. "Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 291-317.
    9. Susan Embretson, 1991. "A multidimensional latent trait model for measuring learning and change," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 495-515, September.
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    Cited by:

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    2. Udo Boehm & Maarten Marsman & Han L. J. Maas & Gunter Maris, 2021. "An Attention-Based Diffusion Model for Psychometric Analyses," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 938-972, December.
    3. Aldo Gardini & Carlo Trivisano & Enrico Fabrizi, 2021. "Bayesian Analysis of ANOVA and Mixed Models on the Log-Transformed Response Variable," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 619-641, June.
    4. Fang Liu & Xiaojing Wang & Roeland Hancock & Ming-Hui Chen, 2022. "Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1290-1317, December.
    5. Daniel W. Heck & Edgar Erdfelder & Pascal J. Kieslich, 2018. "Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 893-918, December.
    6. Qian Wu & Monique Vanerum & Anouk Agten & Andrés Christiansen & Frank Vandenabeele & Jean-Michel Rigo & Rianne Janssen, 2021. "Certainty-Based Marking on Multiple-Choice Items: Psychometrics Meets Decision Theory," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 518-543, June.

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