A Generalized Speed–Accuracy Response Model for Dichotomous Items

We propose a generalization of the speed–accuracy response model (SARM) introduced by Maris and van der Maas (Psychometrika 77:615–633, 2012 ). In these models, the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled. Our generalization...

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Bibliographic Details
Published in:Psychometrika 2018-03, Vol.83 (1), p.109-131
Main Authors: van Rijn, Peter W., Ali, Usama S.
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Assessment
Behavioral Science and Psychology
Generalization
Humanities
Item Response Theory
Law
Psychology
Psychometrics
Rasch model
Simulation
Statistical Theory and Methods
Statistics for Social Sciences
Testing and Evaluation
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Summary:We propose a generalization of the speed–accuracy response model (SARM) introduced by Maris and van der Maas (Psychometrika 77:615–633, 2012 ). In these models, the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled. Our generalization is similar to that of the one-parameter logistic (or Rasch) model to the two-parameter logistic (or Birnbaum) model in item response theory. An expectation–maximization (EM) algorithm for estimating model parameters and standard errors was developed. Furthermore, methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score. The presented methods were evaluated in a small simulation study, the results of which indicated good parameter recovery and reasonable type I error rates for the residuals. Finally, the methods were applied to two real data sets. It was found that the two-parameter SARM showed improved fit compared to the one-parameter SARM in both data sets.
ISSN:0033-3123
1860-0980
DOI:10.1007/s11336-017-9590-9