The InterModel Vigorish as a Lens for Understanding (and Quantifying) the Value of Item Response Models for Dichotomously Coded Items

Benjamin W. Domingue (), Klint Kanopka, Radhika Kapoor, Steffi Pohl, R. Philip Chalmers, Charles Rahal and Mijke Rhemtulla
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Benjamin W. Domingue: Stanford University
Klint Kanopka: Stanford University
Radhika Kapoor: Stanford University
Steffi Pohl: Freie Universität Berlin
R. Philip Chalmers: York University
Charles Rahal: University of Oxford
Mijke Rhemtulla: University of California, Davis

Psychometrika, 2024, vol. 89, issue 3, No 13, 1034-1054

Abstract: Abstract The deployment of statistical models—such as those used in item response theory—necessitates the use of indices that are informative about the degree to which a given model is appropriate for a specific data context. We introduce the InterModel Vigorish (IMV) as an index that can be used to quantify accuracy for models of dichotomous item responses based on the improvement across two sets of predictions (i.e., predictions from two item response models or predictions from a single such model relative to prediction based on the mean). This index has a range of desirable features: It can be used for the comparison of non-nested models and its values are highly portable and generalizable. We use this fact to compare predictive performance across a variety of simulated data contexts and also demonstrate qualitative differences in behavior between the IMV and other common indices (e.g., the AIC and RMSEA). We also illustrate the utility of the IMV in empirical applications with data from 89 dichotomous item response datasets. These empirical applications help illustrate how the IMV can be used in practice and substantiate our claims regarding various aspects of model performance. These findings indicate that the IMV may be a useful indicator in psychometrics, especially as it allows for easy comparison of predictions across a variety of contexts.

Keywords: item response theory (IRT); model fit (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11336-024-09977-2

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