A Speed-Accuracy Response Model with Conditional Dependence Between Items

Abstract

Conditional independence assumptions play an important role in many psychometric models, but can sometimes be too restrictive in modeling process data from educational and psychological tests such as response times. For this reason, a continuous speed-accuracy response model is developed that relaxes the assumption of conditional independence of items given latent proficiency (“local” independence). Our model is a generalization of the speed-accuracy response model developed by Maris and van der Maas (Psychometrika, 77:615-633, 2012) in which a scoring rule incorporating both accuracy and speed of item responses is assumed to produce a sufficient statistic for a latent proficiency variable. The assumption of local independence is dropped in a similar way as in the interaction model developed for dichotomous item responses by Haberman (Multivariate and Mixture Distribution Rasch Models, pp. 201–216. Springer, New York, 2007). Recently, Verhelst (Theoretical and Practical Advances in Computer-Based Educational Measurement, pp. 135–160. Springer, Cham, 2019) discussed similar models in the context of exponential family models for continuous item responses. A pairwise conditional maximum likelihood approach is developed to estimate item parameters. The model is illustrated by an application to data from a listening test.