A New Equating Method Through Latent Variables

  • Inés VarasEmail author
  • Jorge González
  • Fernando A. Quintana
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 265)


Comparability of measurements is an important practice in different fields. In educational measurement, equating methods are used to achieve the goal of having comparable scores from different test forms. Equated scores are obtained using the equating transformation which maps the scores on the scale of one test form into their equivalents on the scale of another for the case of sum scores. Such transformation has been typically computed using continuous approximations of the score distributions, leading to equated scores that are not necessarily defined on the original discrete scale. Considering scores as ordinal random variables, we propose a latent variable formulation based on a flexible Bayesian nonparametric model to perform an equipercentile-like equating that is capable to produce equated scores on the original discrete scale. The performance of our model is assessed using simulated data under the equivalent groups equating design. The results show that the proposed method has better performance with respect to a discrete version of estimated equated scores from traditional equating methods.


Test equating Latent variable representation Bayesian nonparametric model 



Inés Varas was funded by CONICYT Doctorado Nacional grant 21151486. Jorge González was funded by FONDECYT grant 1150233. Fernando A. Quintana was partially funded by FONDECYT grant 1180034. This work was supported by Iniciativa Científica Milenio - Minecon Núcleo Milenio MiDaS.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Inés Varas
    • 1
    • 2
    Email author
  • Jorge González
    • 1
    • 2
  • Fernando A. Quintana
    • 1
  1. 1.Departamento de EstadísticaPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Laboratorio Interdisciplinario de Estadística Social, LIES, Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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