A Race Model for Responses and Response Times in Tests

Area of Science:

• Psychometrics
• Cognitive Psychology
• Mathematical Psychology

Background:

• Traditional latent trait models often lack direct ties to the cognitive processes of test-taking.
• There is a need for psychometric models that better reflect the underlying response mechanisms.

Purpose of the Study:

• To present a new latent trait model that integrates response and response time data.
• To connect psychometric modeling more closely with assumptions about the cognitive response process.

Main Methods:

• The proposed model utilizes two increasing stochastic processes representing knowledge accumulation for correct and incorrect response options.
• These processes function as competing accumulators, with the first to reach a threshold determining the response.
• The resulting response time distribution follows a bivariate Birnbaum Saunders distribution, estimated via marginal maximum likelihood.

Main Results:

• The feasibility of the marginal maximum likelihood estimation approach was confirmed through a simulation study.
• A model fit test was developed and proposed for evaluating the proposed model's performance.
• The model demonstrated its utility in analyzing an empirical dataset.

Conclusions:

• The new model provides a more psychologically interpretable framework for analyzing response and response time data in testing.
• It bridges the gap between statistical modeling and cognitive theories of human performance.
• The proposed estimation and model fit procedures are practical for empirical applications.