A Multidimensional Partially Compensatory Response Time Model on Basis of the Log-Normal Distribution

Jochen Ranger, Christoph König, Benjamin W. Domingue, Jörg-Tobias Kuhn and Andreas Frey
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Jochen Ranger: Martin-Luther-University Halle-Wittenberg
Christoph König: Goethe University Frankfurt
Benjamin W. Domingue: Stanford Graduate School of Education
Jörg-Tobias Kuhn: TU Dortmund University
Andreas Frey: Goethe University Frankfurt

Journal of Educational and Behavioral Statistics, 2024, vol. 49, issue 3, 431-464

Abstract: In the existing multidimensional extensions of the log-normal response time (LNRT) model, the log response times are decomposed into a linear combination of several latent traits. These models are fully compensatory as low levels on traits can be counterbalanced by high levels on other traits. We propose an alternative multidimensional extension of the LNRT model by assuming that the response times can be decomposed into two response time components. Each response time component is generated by a one-dimensional LNRT model with a different latent trait. As the response time components—but not the traits—are related additively, the model is partially compensatory. In a simulation study, we investigate the recovery of the model’s parameters. We also investigate whether the fully and the partially compensatory LNRT model can be distinguished empirically. Findings suggest that parameter recovery is good and that the two models can be distinctly identified under certain conditions. The utility of the model in practice is demonstrated with an empirical application. In the empirical application, the partially compensatory model fits better than the fully compensatory model.

Keywords: response time model; log-normal distribution; partially compensatory model (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:49:y:2024:i:3:p:431-464

DOI: 10.3102/10769986231184153

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