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  • 1.
    Wallmark, Joakim
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Josefsson, Maria
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Wiberg, Marie
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Efficiency analysis of item response theory kernel equating for mixed-format tests2023Ingår i: Applied psychological measurement, ISSN 0146-6216, E-ISSN 1552-3497, Vol. 47, nr 7-8, s. 496-512Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This study aims to evaluate the performance of Item Response Theory (IRT) kernel equating in the context of mixed-format tests by comparing it to IRT observed score equating and kernel equating with log-linear presmoothing. Comparisons were made through both simulations and real data applications, under both equivalent groups (EG) and non-equivalent groups with anchor test (NEAT) sampling designs. To prevent bias towards IRT methods, data were simulated with and without the use of IRT models. The results suggest that the difference between IRT kernel equating and IRT observed score equating is minimal, both in terms of the equated scores and their standard errors. The application of IRT models for presmoothing yielded smaller standard error of equating than the log-linear presmoothing approach. When test data were generated using IRT models, IRT-based methods proved less biased than log-linear kernel equating. However, when data were simulated without IRT models, log-linear kernel equating showed less bias. Overall, IRT kernel equating shows great promise when equating mixed-format tests.

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  • 2.
    Wallmark, Joakim
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Josefsson, Maria
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Wiberg, Marie
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet, Statistik.
    Kernel equating presmoothing methods: an empirical study with mixed-format test forms2023Ingår i: Quantitative psychology: The 87th annual meeting of the psychometric society, Bologna, Italy, 2022 / [ed] Marie Wiberg; Dylan Molenaar; Jorge González; Jee-Seon Kim; Heungsun Hwang, Springer, 2023, s. 49-59Konferensbidrag (Refereegranskat)
    Abstract [en]

    When equating test forms, it is common to presmooth the test score distributions before conducting the equating. In this study, the log-linear and item response theory (IRT) presmoothing methods were compared when equating mixed-format test forms using kernel equating. Test forms from two different high-stakes tests were equated: The Swedish national test in mathematics, using the equivalent group sampling design, and the verbal part of the Swedish SAT test, using the nonequivalent groups with anchor test sampling design. In both cases, the analytical equating standard errors were lower for high and low performing test takers when using IRT presmoothing compared to log-linear presmoothing. Both presmoothing methods resulted in reasonable equated curves. As no true equating transformation is known in a practical setting, using IRT models for presmoothing appears to be a viable alternative to log-linear models when equating mixed-format tests such as the Swedish SAT.

  • 3.
    Wallmark, Joakim
    et al.
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet.
    Ramsay, James O.
    McGill University, Canada.
    Li, Juan
    Ottawa Hospital Research Institute, Canada.
    Wiberg, Marie
    Umeå universitet, Samhällsvetenskapliga fakulteten, Handelshögskolan vid Umeå universitet.
    Analyzing polytomous test data: a comparison between an information-based IRT model and the generalized partial credit model2024Ingår i: Journal of educational and behavioral statistics, ISSN 1076-9986, E-ISSN 1935-1054, Vol. 49, nr 5, s. 753-779Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Item response theory (IRT) models the relationship between the possible scores on a test item against a test taker’s attainment of the latent trait that the item is intended to measure. In this study, we compare two models for tests with polytomously scored items: the optimal scoring (OS) model, a nonparametric IRT model based on the principles of information theory, and the generalized partial credit (GPC) model, a widely used parametric alternative. We evaluate these models using both simulated and real test data. In the real data examples, the OS model demonstrates superior model fit compared to the GPC model across all analyzed datasets. In our simulation study, the OS model outperforms the GPC model in terms of bias, but at the cost of larger standard errors for the probabilities along the estimated item response functions. Furthermore, we illustrate how surprisal arc length, an IRT scale invariant measure of ability with metric properties, can be used to put scores from vastly different types of IRT models on a common scale. We also demonstrate how arc length can be a viable alternative to sum scores for scoring test takers.

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