title: An accumulator model for responses and response times in tests based on the proportional hazards model.
abstract: Latent trait models for responses and response times in tests often lack a substantial interpretation in terms of a cognitive process model. This is a drawback because process models are helpful in clarifying the meaning of the latent traits. In the present paper, a new model for responses and response times in tests is presented. The model is based on the proportional hazards model for competing risks. Two processes are assumed, one reflecting the increase in knowledge and the second the tendency to discontinue. The processes can be characterized by two proportional hazards models whose baseline hazard functions correspond to the temporary increase in knowledge and discouragement. The model can be calibrated with marginal maximum likelihood estimation and an application of the ECM algorithm. Two tests of model fit are proposed. The amenability of the proposed approaches to model calibration and model evaluation is demonstrated in a simulation study. Finally, the model is used for the analysis of two empirical data sets.
authors.affiliation: Department of Psychology, Martin-Luther-University Halle-Wittenberg, Germany.
authors.forename: Jochen
authors.initials: J
authors.lastname: Ranger
authors.forename: Jörg-Tobias
authors.initials: JT
authors.lastname: Kuhn
mesh_terms: D000465:Algorithms; D001245:Association Learning; D004521:Educational Measurement / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D008960:Models, Psychological; D015233:Models, Statistical; D010364:Pattern Recognition, Visual; D011340:Problem Solving; D016016:Proportional Hazards Models; D011581:Psychological Tests / Q000706:statistics & numerical data*; D011589:Psychology, Experimental / Q000706:statistics & numerical data*; D011594:Psychometrics / Q000706:statistics & numerical data*; D011930:Reaction Time
keywords: item response model; proportional hazards model; response time model; test motivation