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Bayesian Nonparametric Monotone Regression of Dynamic Latent Traits in Item Response Theory Models

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  • Yang Liu
  • Xiaojing Wang

    (University of Connecticut)

Abstract

Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain monotone and smooth conditions. To incorporate such conditions and to alleviate the strong parametric assumption on regressing latent trajectories, a flexible nonparametric prior has been introduced to model the dynamic changes of latent traits for item response theory models over the study period. Suitable Bayesian computation schemes are developed for such analysis of the longitudinal and dichotomous item responses. Simulation studies and a real data example from educational testing have been used to illustrate our proposed methods.

Suggested Citation

  • Yang Liu & Xiaojing Wang, 2020. "Bayesian Nonparametric Monotone Regression of Dynamic Latent Traits in Item Response Theory Models," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 274-296, June.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:3:p:274-296
    DOI: 10.3102/1076998619887913
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    References listed on IDEAS

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    1. Ongaro, Andrea & Cattaneo, Carla, 2004. "Discrete random probability measures: a general framework for nonparametric Bayesian inference," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 33-45, March.
    2. Lizhen Lin & David B. Dunson, 2014. "Bayesian monotone regression using Gaussian process projection," Biometrika, Biometrika Trust, vol. 101(2), pages 303-317.
    3. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2011. "Assessment of School Performance Through a Multilevel Latent Markov Rasch Model," Journal of Educational and Behavioral Statistics, , vol. 36(4), pages 491-522, August.
    4. van Dyk, David A. & Park, Taeyoung, 2008. "Partially Collapsed Gibbs Samplers: Theory and Methods," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 790-796, June.
    5. S. McKay Curtis & Sujit K. Ghosh, 2011. "A variable selection approach to monotonic regression with Bernstein polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 961-976, February.
    6. Taeryon Choi & Hea-Jung Kim & Seongil Jo, 2016. "Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2751-2771, November.
    7. E.S. Tan & A.W. Ambergen & R.J.M.M. Does & Tj. Imbos, 1999. "Approximations of Normal IRT Models for Change," Journal of Educational and Behavioral Statistics, , vol. 24(2), pages 208-223, June.
    8. Martin, Andrew D. & Quinn, Kevin M., 2002. "Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the U.S. Supreme Court, 1953–1999," Political Analysis, Cambridge University Press, vol. 10(2), pages 134-153, April.
    9. W. Albers & R. Does & Tj. Imbos & M. Janssen, 1989. "A stochastic growth model applied to repeated tests of academic knowledge," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 451-466, September.
    10. Susan Embretson, 1991. "A multidimensional latent trait model for measuring learning and change," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 495-515, September.
    11. Björn Bornkamp & Katja Ickstadt, 2009. "Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose–Response Analysis," Biometrics, The International Biometric Society, vol. 65(1), pages 198-205, March.
    12. van Dorp J.R. & Kotz S., 2002. "The Standard Two-Sided Power Distribution and its Properties: With Applications in Financial Engineering," The American Statistician, American Statistical Association, vol. 56, pages 90-99, May.
    13. Thomas S. Shively & Thomas W. Sager & Stephen G. Walker, 2009. "A Bayesian approach to non‐parametric monotone function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 159-175, January.
    14. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    15. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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