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

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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.

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Notes

  1. Word frequency is the how often a word occurs in natural written discourse. It is simply the frequency of occurrence in a large corpora such as a large collection newspaper and magazine articles (Kucera & Francis, 1967). For instance, AJAR occurs less than once per million words of text, ECHO occurs 34 times per million words of text, and CITY occurs over 200 times per million words of text.

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Acknowledgements

This research is supported by National Science Foundation Grants SES-1024080 and BCS-1240359 (JNR) and Australian Research Council Professorial Fellowship (AH).

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Authors and Affiliations

  1. University of Missouri, Columbia, MO, USA

    Jeffrey N. Rouder & Jordan M. Province

  2. University of Groningen, Groningen, The Netherlansa

    Richard D. Morey

  3. Depaul University, Chicago, IL, USA

    Pablo Gomez

  4. University of Newcastle, Newcastle, Australia

    Andrew Heathcote

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  1. Jeffrey N. Rouder
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  2. Jordan M. Province
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  4. Pablo Gomez
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Correspondence to Jeffrey N. Rouder.

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Rouder, J.N., Province, J.M., Morey, R.D. et al. The Lognormal Race: A Cognitive-Process Model of Choice and Latency with Desirable Psychometric Properties. Psychometrika 80, 491–513 (2015). https://doi.org/10.1007/s11336-013-9396-3

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