Disentangling Different Aspects of Change in Tests with the D-Diffusion Model

• Published in: Multivariate behavioral research Vol. 58; no. 5; pp. 1039 - 1055
• Main Authors: Ranger, Jochen, Wolgast, Anett, Much, Sören, Mutak, Augustin, Krause, Robert, Pohl, Steffi
• Format: Journal Article
• Language: English
• Published: United States Routledge 03.09.2023; Taylor & Francis Ltd
• Subjects: change; D-Diffusion model; Diffusion rate; Drift rate; growth curve model; item position effect; Item response theory; Mathematical models; Parameter estimation; response time; Spatial data; growth curve model; item position effect; response time; D-Diffusion model; change
• ISSN: 0027-3171; 1532-7906
• DOI: 10.1080/00273171.2023.2171356

Diffusion-based item response theory models are measurement models that link parameters of the diffusion model (drift rate, boundary separation) to latent traits of test takers. Similar to standard latent trait models, they assume the invariance of the test takers' latent traits during a test. Previous research, however, suggests that traits change as test takers learn or decrease their effort. In this paper, we combine the diffusion-based item response theory model with a latent growth curve model. In the model, the latent traits of each test taker are allowed to change during the test until a stable level is reached. As different change processes are assumed for different traits, different aspects of change can be separated. We discuss different versions of the model that make different assumptions about the form (linear versus quadratic) and rate (fixed versus individual-specific) of change. In order to fit the model to data, we propose a Bayes estimator. Parameter recovery is investigated in a simulation study. The study suggests that parameter recovery is good under certain conditions. We illustrate the application of the model to data measuring visuo-spatial perspective-taking.