Abstract
This chapter describes the kernel equating framework. The five steps that characterize kernel equating are illustrated using the Math20EG, Math20SG, CBdata, and KB36 data sets that were introduced in Chap. 2 and which have been previously analyzed in the literature. We also illustrate the methods using the ADM admissions test data set. The R packages kequate (Andersson et al., J Stat Softw 55(6):1–25, 2013) and SNSequate (González, J Stat Softw 59(7), 1–30, 2014) are used throughout the chapter.
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Notes
- 1.
Further details about \(\boldsymbol{C}\) matrices are given in Appendix B.2.
- 2.
Negative score values can arise for instance when in a multiple choice test, a fraction of the total score in the test is discounted for each wrong answer in the test.
- 3.
Note that this is only true for the EG design. For other designs, the vector of score probabilities has to be further transformed using the design functions in order to obtain \(\hat{r}_{j}\) and \(\hat{s}_{k}\).
- 4.
Although variances instead of standard deviations are plotted in the right panel of Fig. 4.5.
- 5.
It might be possible to obtain estimated score probabilities from fitted frequencies for designs different than the EG, but additional steps might be necessary (i.e., the DF should be explicitly programmed and applied).
- 6.
Estimated score probabilities are obtained by making a call to the loglin.smooth() function.
- 7.
Values from lines 6 to 75 have been omitted in order to save space.
- 8.
The quantity inside the norm sign in Eq. (4.15) is called an SEE vector.
- 9.
Values from lines 6–75 have been omitted to save space.
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González, J., Wiberg, M. (2017). Kernel Equating. In: Applying Test Equating Methods. Methodology of Educational Measurement and Assessment. Springer, Cham. https://doi.org/10.1007/978-3-319-51824-4_4
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