Normal Models for Response Times on Test Items (CT-04-08)
by Wim J. van der Linden, University of Twente, Enschede, The Netherlands
An important source of information that becomes automatically available when tests are delivered by computer is test takers' response times on items. This source of information has the potential to improve many of our routine operations in testing, including calculating certain item statistics, assembling tests, selecting items for administration to a test taker in an adaptive test, diagnosing misfitting test taker and test item behavior, and test equating.
It is only possible to use response time data when we have a psychometric model that allows us to separate the effects of persons and items on response times. In this paper, we investigate alternative response-time models based on the normal distribution. The models are: (1) a normal model for individual response-time distributions with parameters for the speed of the person and the time intensity and discriminating power of the item; (2) a lognormal model sharing the same parameters, and (3) versions of these models with a common discrimination parameter for all items.
We developed statistical methods and computer programs for parameter estimation and model validation for these models. The methods were used in an empirical study of response times for the adaptive version of a test from the Armed Services Vocational Aptitude Battery (ASVAB). The statistical methods showed excellent behavior. In addition, the lognormal model showed an excellent fit to the response times. This model will be our choice in future work on a multilevel model that should allow us to analyze structural relations between speed and accuracy on test items and to derive empirical information from response times to improve item calibration and item fit analyses.