An accumulator model for responses and response times in tests based on the proportional hazards model

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 respo...

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Bibliographic Details
Published in:British journal of mathematical & statistical psychology 2014-11, Vol.67 (3), p.388-407
Main Authors: Ranger, Jochen, Kuhn, Jörg-Tobias
Format: Article
Language:English
Subjects:
Algorithms
Association Learning
Cognitive models
Educational Measurement - statistics & numerical data
Humans
item response model
Iterative methods
Likelihood Functions
Maximum likelihood method
Models, Psychological
Models, Statistical
Pattern Recognition, Visual
Problem Solving
proportional hazards model
Proportional Hazards Models
Psychological Tests - statistics & numerical data
Psychology, Experimental - statistics & numerical data
Psychometrics - statistics & numerical data
Reaction Time
response time model
Risk assessment
Simulation
test motivation
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Summary: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.
ISSN:0007-1102
2044-8317
DOI:10.1111/bmsp.12025