Skip to main content
SpringerLink
Log in
Book cover

Applying Test Equating Methods pp 157–178Cite as

Recent Developments in Equating

  • Chapter
  • First Online:

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

Abstract

This chapter briefly describes some recent developments in test equating and provides examples of how they are performed using 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). The chapter begins with recent developments within the kernel equating framework, including different bandwidth selection methods, the use of different kernels in the continuization step, and IRT kernel equating. A Bayesian approach to test equating and the assessment of equating transformations are also discussed. The chapter ends with some concluding reflections on the future of equating research connected to the use of R.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    More details are given in Sect. B.8.

  2. 2.

    Results for test scores (2, …, 78) have been omitted.

  3. 3.

    In the examples that follow, the dependence is accounted in the form of a regression on the \(\boldsymbol{z}\) covariates.

  4. 4.

    The BNP.eq() function makes use of other functions from the R package DPpackage (Jara et al. 2011), which is also downloaded and installed when installing SNSequate.

  5. 5.

    Running the BNP.eq() function can take a considerable amount of computation time.

  6. 6.

    Note that the covariates that are not directly involved in the equating of interest are automatically integrated out by the function.

References

  • Andersson, B. (2016). Asymptotic standard errors of observed-score equating with polytomous IRT models. Journal of Educational Measurement, 53(4), 459–477.

    Article  Google Scholar 

  • Andersson, B., Bränberg, K., & Wiberg, M. (2013). Performing the kernel method of test equating with the package kequate. Journal of Statistical Software, 55(6), 1–25.

    Article  Google Scholar 

  • Andersson, B., & von Davier, A. A. (2014). Improving the bandwidth selection in kernel equating. Journal of Educational Measurement, 51(3), 223–238.

    Google Scholar 

  • Andersson, B., & Wiberg, M. (2014). IRT observed-score kernel equating with the R package kequate. R: Vignette. Retrieved from https://cran.r-project.org/web/packages/kequate/vignettes/irtguide.pdf

  • Andersson, B., & Wiberg, M. (2016). Item response theory observed-score kernel equating. Psychometrika. doi: 10.1007/s11336--016--9528--7.

    Google Scholar 

  • Barrientos, A. F., Jara, A., & Quintana, F. A. (2012). On the support of MacEachern’s dependent Dirichlet processes and extensions. Bayesian Analysis, 7, 277–310.

    Google Scholar 

  • Chalmers, R. P. (2012). Mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1–29.

    Google Scholar 

  • Cid, J. A., & von Davier, A. A. (2015). Examining potential boundary bias effects in kernel smoothing on equating: An introduction for the adaptive and Epanechnikov kernels. Applied Psychological Measurement, 39(3), 208–222.

    Google Scholar 

  • Dorans, N., & Feigenbaum, M. (1994). Equating issues engendered by changes to the SAT and PSAT/NMSQT. Technical issues related to the introduction of the new SAT and PSAT/NMSQT (pp. 91–122).

    Google Scholar 

  • Epanechnikov, V. (1969). Non-parametric estimation of a multivariate probability density. Theory of Probability and Its Applications, 14, 153–158.

    Article  Google Scholar 

  • Gelman, A., Carlin, J., Stern, H., & Rubin, D. (2003). Bayesian data analysis (2nd ed.). Boca Raton: Chapman and Hall.

    Google Scholar 

  • Ghosh, J., & Ramamoorthi, R. (2003). Bayesian nonparametrics. New York: Springer.

    Google Scholar 

  • González, J. (2014). SNSequate: Standard and nonstandard statistical models and methods for test equating. Journal of Statistical Software, 59(7), 1–30.

    Article  Google Scholar 

  • González, J., Barrientos, A. F., & Quintana, F. A. (2015). A dependent Bayesian nonparametric model for test equating. In R. Millsap, D. Bolt, L. van der Ark, & W.-C. Wang (Eds.), Quantitative psychology research (pp. 213–226). Cham: Springer International Publishing.

    Google Scholar 

  • González, J., Barrientos, A. F., & Quintana, F. A. (2015). Bayesian nonparametric estimation of test equating functions with covariates. Computational Statistics & Data Analysis, 89, 222–244.

    Google Scholar 

  • González, J., & von Davier, A. A. (2017). An illustration of the Epanechnikov and adaptive continuization methods in kernel equating. In L. A. van der Ark, M. Wiberg, S. A. Culpeppe, J. A. Douglas, & W.-C. Wang (Eds.), Quantitative psychology – 81st annual meeting of the psychometric society, Asheville, North Carolina, 2016. New York: Springer.

    Google Scholar 

  • Häggström, J., & Wiberg, M. (2014). Optimal bandwidth selection in observed-score kernel equating. Journal of Educational Measurement, 51(2), 201–211.

    Article  Google Scholar 

  • Hall, P., Marron, J., & Park, B. U. (1992). Smoothed cross-validation. Probability Theory and Related Fields, 92(1), 1–20.

    Google Scholar 

  • Harris, D. J., & Crouse, J. D. (1993). A study of criteria used in equating. Applied Measurement in Education, 6(3), 195–240.

    Google Scholar 

  • Hjort, N. L., Holmes, C., Müller, P., & Walker, S. (2010). Bayesian nonparametrics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Jara, A., Hanson, T., Quintana, F., Müller, P., & Rosner, G. (2011). Dppackage: Bayesian non-and semi-parametric modelling in R. Journal of Statistical Software, 40, 1–30.

    Article  Google Scholar 

  • Karabatsos, G., & Walker, S. (2009). A Bayesian nonparametric approach to test equating. Psychometrika, 74(2), 211–232.

    Article  Google Scholar 

  • Liang, T., & von Davier, A. A. (2014). Cross-validation: An alternative bandwidth-selection method in kernel equating. Applied Psychological Measurement, 38(4), 281–295.

    Google Scholar 

  • Lord, F., & Wingersky, M. (1984). Comparison of IRT true-score and equipercentile observed-score “equatings”. Applied Psychological Measurement, 8(4), 453–461.

    Article  Google Scholar 

  • Müller, P., & Quintana, F. (2004). Nonparametric Bayesian data analysis. Statistical Science, 19, 95–110.

    Article  Google Scholar 

  • Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.

    Article  Google Scholar 

  • Rizopoulos, D. (2006). ltm: An R package for latent variable modeling and item response theory analyses. Journal of Statistical Software, 17(5), 1–25.

    Article  Google Scholar 

  • Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. (Psychometrika Monograph No. 17). Richmond, VA: Psychometric Society.

    Google Scholar 

  • Silverman, B. (1986). Density estimation for statistics and data analysis (Vol. 3). London: Chapman and Hall.

    Book  Google Scholar 

  • Thissen, D., Pommerich, M., Billeaud, K., & Williams, V. S. L. (1995). Item response theory for scores on tests including polytomous items with ordered responses. Applied Psychological Measurement, 19(1), 39–49.

    Google Scholar 

  • Wiberg, M., & González, J. (2016). Statistical assessment of estimated transformations in observed-score equating. Journal of Educational Measurement, 53(1), 106–125.

    Article  Google Scholar 

  • Yuan, K.-H., Cheng, Y., & Patton, J. (2014). Information matrices and standard errors for MLEs of item parameters in IRT. Psychometrika, 79(2), 232–254.

    Article  Google Scholar 

Download references

Author information

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

Authors
  1. Jorge González
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marie Wiberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

González, J., Wiberg, M. (2017). Recent Developments in Equating. In: Applying Test Equating Methods. Methodology of Educational Measurement and Assessment. Springer, Cham. https://doi.org/10.1007/978-3-319-51824-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-51824-4_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51822-0

  • Online ISBN: 978-3-319-51824-4

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation