IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v89y2015icp222-244.html
   My bibliography  Save this article

Bayesian nonparametric estimation of test equating functions with covariates

Author

Listed:
  • González, Jorge
  • Barrientos, Andrés F.
  • Quintana, Fernando A.

Abstract

Equating is an important step in the process of collecting, analyzing, and reporting test scores in any program of assessment. Methods of equating utilize functions to transform scores on two or more versions of a test, so that they can be compared and used interchangeably. In common practice, traditional methods of equating use either parametric or semi-parametric models where, apart from the test scores themselves, no additional information is used to estimate the equating transformation function. A flexible Bayesian nonparametric model for test equating which allows the use of covariates in the estimation of the score distribution functions that lead to the equating transformation is proposed. A major feature of this approach is that the complete shape of the scores distribution may change as a function of the covariates. As a consequence, the form of the equating transformation can change according to covariate values. Applications of the proposed model to real and simulated data are discussed and compared to other current methods of equating.

Suggested Citation

  • González, Jorge & Barrientos, Andrés F. & Quintana, Fernando A., 2015. "Bayesian nonparametric estimation of test equating functions with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 222-244.
    • Handle: RePEc:eee:csdana:v:89:y:2015:i:c:p:222-244
    DOI: 10.1016/j.csda.2015.03.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315000808
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.03.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. George Karabatsos & Stephen Walker, 2009. "A Bayesian Nonparametric Approach to Test Equating," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 211-232, June.
    3. Bigelow, Jamie L. & Dunson, David B., 2009. "Bayesian Semiparametric Joint Models for Functional Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 26-36.
    4. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    5. Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393, September.
    6. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    7. Smith, Brian J., 2007. "boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i11).
    8. Sara Wade & Stephen G. Walker & Sonia Petrone, 2014. "A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 580-605, September.
    9. Lijoi, Antonio & Prunster, Igor & Walker, Stephen G., 2005. "On Consistency of Nonparametric Normal Mixtures for Bayesian Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1292-1296, December.
    10. Alina Davier, 2013. "Observed-Score Equating: An Overview," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 605-623, October.
    11. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Inés M. Varas & Jorge González & Fernando A. Quintana, 2020. "A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 639-666, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    2. repec:jss:jstsof:40:i05 is not listed on IDEAS
    3. Sonia Petrone & Michele Guindani & Alan E. Gelfand, 2009. "Hybrid Dirichlet mixture models for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 755-782, September.
    4. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    5. Leisen, Fabrizio, 2013. "A multivariate extension of a vector of Poisson- Dirichlet processes," DES - Working Papers. Statistics and Econometrics. WS ws132220, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    7. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    8. Hatjispyros, Spyridon J. & Merkatas, Christos & Nicoleris, Theodoros & Walker, Stephen G., 2018. "Dependent mixtures of geometric weights priors," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 1-18.
    9. Andrés F. Barrientos & Alejandro Jara & Fernando A. Quintana, 2017. "Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 806-825, April.
    10. Gutiérrez, Luis & Mena, Ramsés H. & Ruggiero, Matteo, 2016. "A time dependent Bayesian nonparametric model for air quality analysis," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 161-175.
    11. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    13. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    14. Bruno Scarpa & David B. Dunson, 2014. "Enriched Stick-Breaking Processes for Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 647-660, June.
    15. Trippa, Lorenzo & Muliere, Pietro, 2009. "Bayesian nonparametric binary regression via random tessellations," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2273-2280, November.
    16. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    17. Inés M. Varas & Jorge González & Fernando A. Quintana, 2020. "A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 639-666, December.
    18. Chen, Kunzhi & Shen, Weining & Zhu, Weixuan, 2023. "Covariate dependent Beta-GOS process," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    19. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    20. Richardson, Robert & Kottas, Athanasios & Sansó, Bruno, 2017. "Flexible integro-difference equation modeling for spatio-temporal data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 182-198.
    21. Huang, Yifan & Meng, Shengwang, 2020. "A Bayesian nonparametric model and its application in insurance loss prediction," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 84-94.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:89:y:2015:i:c:p:222-244. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.