Advertisement

Psychometrika

, Volume 77, Issue 4, pp 615–633 | Cite as

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

  • Gunter Maris
  • Han van der Maas
Article

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.

Key words

item response theory response times two-parameter logistic model scoring rule 

References

  1. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F.M. Lord & M.R. Novick (Eds.), Statistical theories of mental test scores (pp. 395–479). Reading: Addison-Wesley. Google Scholar
  2. Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51. CrossRefGoogle Scholar
  3. de Leeuw, J. (1994). Block-relaxation algorithms in statistics. In H.H. Bock, W. Lenski, & M.M. Richter (Eds.), Information systems and data analysis (pp. 308–325). Berlin: Springer. CrossRefGoogle Scholar
  4. de Leeuw (J.2006). Some majorization techniques (Tech. Rep. No. 2006032401). Department of statistics, UCLA. Google Scholar
  5. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, 39, 1–38. Google Scholar
  6. Dennis, I., & Evans, J. (1996). The speed-error trade-off problem in psychometric testing. British Journal of Psychology, 87, 105–129. CrossRefGoogle Scholar
  7. Hunter, D., & Lange, K. (2004). A tutorial on MM algorithms. American Statistician, 58(1), 30–37. CrossRefGoogle Scholar
  8. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: The Danish Institute of Educational Research. (Expanded edition, 1980. Chicago: The University of Chicago Press). Google Scholar
  9. Tuerlinckx, F., & De Boeck, P. (2005). Two interpretations of the discrimination parameter. Psychometrika, 70(4), 629–650. CrossRefGoogle Scholar
  10. van der Linden, W.J. (2007). A hierarchical framework for modeling speed and accuracy on test items. Psychometrika, 72, 287–308. CrossRefGoogle Scholar
  11. Van der Maas, H.L., Molenaar, D., Maris, G., Kievit, R.A., & Borsboom, D. (2011). Cognitive psychology meets psychometric theory: on the relation between process models for decision making and latent variable models for individual differences. Psychological Review, 118(2), 339–356. PubMedCrossRefGoogle Scholar
  12. Van der Maas, H.L., & Wagenmakers, E.J. (2005). A psychometric analysis of chess expertise. The American Journal of Psychology, 118(1), 29–60. PubMedGoogle Scholar
  13. van Ruitenburg, J. (2005). Algorithms for parameter estimation in the Rasch model. Unpublished master’s thesis, Erasmus University. Google Scholar
  14. Verhelst, N.D., & Glas, C.A.W. (1995). The one parameter logistic model: OPLM. In G.H. Fischer & I.W. Molenaar (Eds.), Rasch models: foundations, recent developments and applications (pp. 215–238). New York: Springer. Google Scholar
  15. Wickelgren, W. (1977). Speed-accuracy tradeoff and information processing dynamics. Acta Psychologica, 41, 67–85. CrossRefGoogle Scholar

Copyright information

© The Psychometric Society 2012

Authors and Affiliations

  1. 1.Cito – University of AmsterdamArnhemThe Netherlands
  2. 2.University of AmsterdamAmsterdamThe Netherlands

Personalised recommendations