 A Lognormal Model for Response Times on Test ItemsWim J. van der Linden Journal of Educational and Behavioral Statistics, 2006, vol. 31, issue 2, 181-204 Abstract: A lognormal model for the response times of a person on a set of test items is investigated. The model has a parameter structure analogous to the two-parameter logistic response models in item response theory, with a parameter for the speed of each person as well as parameters for the time intensity and discriminating power of each item. It is shown how these parameters can be estimated by a Markov chain Monte Carlo method (Gibbs sampler). The method was used to analyze response times for the adaptive version of a test from the Armed Services Vocational Aptitude Battery. The same data set was used to test the validity of the model against a normal model using posterior predictive checks on the response times. The lognormal model showed an excellent fit to the data, whereas the normal model seemed unable to allow for a characteristic skewness of the response time distributions. The addition of an equality constraint on the discrimination parameters led only to a slight loss of fit. The potential use of the model for improving the daily practice of testing is indicated. Keywords: computer-based testing; lognormal distribution; Markov chain Monte Carlo estimation; normal distribution; response times (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:31:y:2006:i:2:p:181-204 DOI: 10.3102/10769986031002181 Access Statistics for this article More articles in Journal of Educational and Behavioral Statistics |
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