This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by van der Linden, W. J. Search for Related Content Social Bookmarking                         What's this?

A Lognormal Model for Response Times on Test Items

University of Twente

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.

Key Words: computer-based testing • lognormal distribution • Markov chain Monte Carlo estimation • normal distribution • response times

Journal of Educational and Behavioral Statistics, Vol. 31, No. 2, 181-204 (2006)
DOI: 10.3102/10769986031002181


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?

This article has been cited by other articles:

				W. J. van der Linden A Bivariate Lognormal Response-Time Model for the Detection of Collusion Between Test Takers Journal of Educational and Behavioral Statistics, September 1, 2009; 34(3): 378 - 394. [Abstract] [Full Text] [PDF]

				W. J. van der Linden Predictive Control of Speededness in Adaptive Testing Applied Psychological Measurement, January 1, 2009; 33(1): 25 - 41. [Abstract] [PDF]

				W. J. van der Linden Using Response Times for Item Selection in Adaptive Testing Journal of Educational and Behavioral Statistics, March 1, 2008; 33(1): 5 - 20. [Abstract] [Full Text] [PDF]