Parametric Bootstrap Mantel‐Haenszel Statistic for Aggregated Testlet Effects.
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| Title: | Parametric Bootstrap Mantel‐Haenszel Statistic for Aggregated Testlet Effects. |
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| Authors: | Lim, Youn Seon1 (AUTHOR) limyo@ucmail.uc.edu |
| Source: | Journal of Educational Measurement. Dec2025, Vol. 62 Issue 4, p503-530. 28p. |
| Subject Terms: | *Problem solving, Statistical bootstrapping, Simulation methods & models, Statistical hypothesis testing, Mathematical statistics |
| Abstract: | While testlets have proven useful for assessing complex skills, the stem shared by multiple items often induces correlations between responses, leading to violations of local independence (LI), which can result in biased parameter and ability estimates. Diagnostic procedures for detecting testlet effects typically involve model comparisons testing for the inclusion of extra testlet parameters or, at the item level, testing for pairwise LI. Rosenbaum's adaptation of the Mantel‐Haenszel (MH) χ2$\chi ^2$‐statistic belongs to the latter category. The MH χ2$\chi ^2$‐statistic has also been used in cognitive diagnosis for detecting violations of LI and for the identification of testlet effects. However, this approach is not without limitations, as it lacks a rationale for integrating multiple pairwise MH χ2$\chi ^2$‐statistics and any notion of the sampling distribution of such an integrated statistic. In this article, a procedure for integrating multiple pairwise MH χ2$\chi ^2$‐statistics to evaluate testlet effects in cognitive diagnosis is proposed. The unknown sampling distribution issue is addressed by implementing a parametric bootstrap resampling scheme. Results from simulation studies demonstrate the performance of the proposed parametric bootstrap testlet MH χ2$\chi ^2$‐statistic, and its application to the 2015 PISA Collaborative Problem Solving (CPS) data set illustrates the method's practical merits. [ABSTRACT FROM AUTHOR] |
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| Database: | Education Research Complete |
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| Abstract: | While testlets have proven useful for assessing complex skills, the stem shared by multiple items often induces correlations between responses, leading to violations of local independence (LI), which can result in biased parameter and ability estimates. Diagnostic procedures for detecting testlet effects typically involve model comparisons testing for the inclusion of extra testlet parameters or, at the item level, testing for pairwise LI. Rosenbaum's adaptation of the Mantel‐Haenszel (MH) χ2$\chi ^2$‐statistic belongs to the latter category. The MH χ2$\chi ^2$‐statistic has also been used in cognitive diagnosis for detecting violations of LI and for the identification of testlet effects. However, this approach is not without limitations, as it lacks a rationale for integrating multiple pairwise MH χ2$\chi ^2$‐statistics and any notion of the sampling distribution of such an integrated statistic. In this article, a procedure for integrating multiple pairwise MH χ2$\chi ^2$‐statistics to evaluate testlet effects in cognitive diagnosis is proposed. The unknown sampling distribution issue is addressed by implementing a parametric bootstrap resampling scheme. Results from simulation studies demonstrate the performance of the proposed parametric bootstrap testlet MH χ2$\chi ^2$‐statistic, and its application to the 2015 PISA Collaborative Problem Solving (CPS) data set illustrates the method's practical merits. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 00220655 |
| DOI: | 10.1111/jedm.12440 |
