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Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy

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  • Gunter Maris
  • Han Maas

Abstract

Starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy, and a definite trade-off between speed and accuracy, a response model is derived. Since the scoring rule is interpreted as a sufficient statistic, the model belongs to the exponential family. The various marginal and conditional distributions for response accuracy and response time are derived, and it is shown how the model parameters can be estimated. The model for response accuracy is found to be the two-parameter logistic model. It is found that the time limit determines the item discrimination, and this effect is illustrated with the Amsterdam Chess Test II. Copyright The Psychometric Society 2012

Suggested Citation

  • Gunter Maris & Han Maas, 2012. "Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 615-633, October.
    • Handle: RePEc:spr:psycho:v:77:y:2012:i:4:p:615-633
    DOI: 10.1007/s11336-012-9288-y
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    References listed on IDEAS

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    1. Hunter D.R. & Lange K., 2004. "A Tutorial on MM Algorithms," The American Statistician, American Statistical Association, vol. 58, pages 30-37, February.
    2. Francis Tuerlinckx & Paul Boeck, 2005. "Two interpretations of the discrimination parameter," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 629-650, December.
    3. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    4. 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.
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    Citations

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    Cited by:

    1. Frederik Coomans & Abe Hofman & Matthieu Brinkhuis & Han L J van der Maas & Gunter Maris, 2016. "Distinguishing Fast and Slow Processes in Accuracy - Response Time Data," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-19, May.
    2. Inhan Kang & Paul Boeck & Roger Ratcliff, 2022. "Modeling Conditional Dependence of Response Accuracy and Response Time with the Diffusion Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 725-748, June.
    3. Maria Bolsinova & Jesper Tijmstra, 2016. "Posterior Predictive Checks for Conditional Independence Between Response Time and Accuracy," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 123-145, April.
    4. Shiyu Wang & Yinghan Chen, 2020. "Using Response Times and Response Accuracy to Measure Fluency Within Cognitive Diagnosis Models," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 600-629, September.
    5. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    6. Nathan D. Minchen & Jimmy de la Torre & Ying Liu, 2017. "A Cognitive Diagnosis Model for Continuous Response," Journal of Educational and Behavioral Statistics, , vol. 42(6), pages 651-677, December.
    7. Peter W. Rijn & Usama S. Ali, 2018. "A Generalized Speed–Accuracy Response Model for Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 109-131, March.
    8. Sandip Sinharay & Peter W. van Rijn, 2020. "Assessing Fit of the Lognormal Model for Response Times," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 534-568, October.
    9. Yi-Hsuan Lee & Zhiliang Ying, 2015. "A Mixture Cure-Rate Model for Responses and Response Times in Time-Limit Tests," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 748-775, September.

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