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Item Response Theory Equating

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Applying Test Equating Methods

Part of the book series: Methodology of Educational Measurement and Assessment ((MEMA))

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Abstract

In this chapter, different methods of Item Response Theory (IRT) linking and equating will be discussed and illustrated using the SNSequate (González, J Stat Softw 59(7):1–30, 2014) and equateIRT (Battauz, J Stat Softw 68(7):1–22, 2015) packages. Other useful packages include ltm (Rizopoulos, J Stat Softw 17(5):1–25, 2006) and mirt (Chalmers, J Stat Softw, 48(6):1–29, 2012), which allow the user to model response data using different IRT models. IRT objects obtained from the latter packages can also be read into equateIRT and kequate (Andersson et al., J Stat Softw, 55(6):1–25, 2013) to perform IRT equating and linking.

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Notes

  1. 1.

    The model shown in Example 1.2 corresponds to the fixed-effects version of IRT models. For more details on the difference between the fixed-effects version and the random-effects version of the model that is presented here, see San Martín et al. (2015).

  2. 2.

    When multiple test forms are to be linked, the argument coef needs a list of matrices containing the item parameter estimates corresponding to each test form.

  3. 3.

    In this case, an internal call to irt.link() is made.

  4. 4.

    Note that the item parameter estimates shown in Table 6.10 in Kolen and Brennan (2014) are already rescaled. This is why we have set the equating coefficients as A=1 and B=0 so that comparable results with those obtained in Kolen and Brennan (2014) are obtained.

  5. 5.

    Figure 6.6 in Kolen and Brennan (2014) also shows the curve for frequency estimation equating. This curve can easily be obtained and added using the equate package as illustrated in Chap. 3

  6. 6.

    Because a Rasch model is used to fit the 0/1 data, item discrimination parameters are fixed to 1 and guessing parameters fixed to 0.

  7. 7.

    Some columns in the output are omitted.

  8. 8.

    The mirt() function implement a general four parameter model from which the 1PL, 2PL and 3PL models are particular cases. The discrimination, difficulty and guessing parameters are denoted by a1, d, and g, respectively, whereas a fourth upper asymptote parameter is denoted by u. In the case of the Rasch model, a1=u=1 and c=0.

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Authors and Affiliations

  1. Faculty of Mathematics, Pontificia Universidad CatÓlica de Chile, Santiago, Chile

    Jorge González

  2. Department of Statistics, Umeå School of Business and Economics, Umeå University, Umeå, Sweden

    Marie Wiberg

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  1. Jorge González
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  2. Marie Wiberg
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González, J., Wiberg, M. (2017). Item Response Theory Equating. In: Applying Test Equating Methods. Methodology of Educational Measurement and Assessment. Springer, Cham. https://doi.org/10.1007/978-3-319-51824-4_5

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  • DOI: https://doi.org/10.1007/978-3-319-51824-4_5

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