title: Modelling Conditional Dependence Between Response Time and Accuracy.
abstract: The assumption of conditional independence between response time and accuracy given speed and ability is commonly made in response time modelling. However, this assumption might be violated in some cases, meaning that the relationship between the response time and the response accuracy of the same item cannot be fully explained by the correlation between the overall speed and ability. We propose to explicitly model the residual dependence between time and accuracy by incorporating the effects of the residual response time on the intercept and the slope parameter of the IRT model for response accuracy. We present an empirical example of a violation of conditional independence from a low-stakes educational test and show that our new model reveals interesting phenomena about the dependence of the item properties on whether the response is relatively fast or slow. For more difficult items responding slowly is associated with a higher probability of a correct response, whereas for the easier items responding slower is associated with a lower probability of a correct response. Moreover, for many of the items slower responses were less informative for the ability because their discrimination parameters decrease with residual response time.
authors.affiliation: Utrecht University, Utrecht, The Netherlands. m.a.bolsinova@uva.nl.|CITO, Dutch National Institute for Educational Measurement, Arnhem, The Netherlands. m.a.bolsinova@uva.nl.|Department of Psychology, University of Amsterdam, Nieuweachtergracht 129, 1018 WS , Amsterdam, The Netherlands. m.a.bolsinova@uva.nl.
authors.forename: Maria
authors.initials: M
authors.lastname: Bolsinova
authors.affiliation: Ohio State University, Columbus, OH, USA.|KU Leuven, Leuven, Belgium.
authors.forename: Paul
authors.initials: P
authors.lastname: de Boeck
authors.affiliation: Tilburg University, Tilburg, The Netherlands.
authors.forename: Jesper
authors.initials: J
authors.lastname: Tijmstra
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008960:Models, Psychological; D015233:Models, Statistical; D011930:Reaction Time; D018401:Sample Size
keywords: conditional independence; hierarchical model; item response theory; response times