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Flexible Bayesian Models for Inferences From Coarsened, Group-Level Achievement Data

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  • J. R. Lockwood
  • Katherine E. Castellano

    (Educational Testing Service)

  • Benjamin R. Shear

    (University of Colorado Boulder)

Abstract

This article proposes a flexible extension of the Fay–Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon, Shear, Castellano, and Ho by allowing group parameters to be modeled with regressions on group-level covariates, and residuals modeled using the flexible exponential family of distributions recommended by Efron. We demonstrate that the alternative modeling framework, termed the “Fay–Herriot heteroskedastic ordered probit†(FH-HETOP) model, is useful for mitigating some of the challenges with direct maximum likelihood estimators from the HETOP model. We conduct a simulation study to compare the costs and benefits of several methods for using the FH-HETOP model to estimate group parameters and functions of them, including posterior means, constrained Bayes estimators, and the “triple goal†estimators of Shen and Louis. We also provide an application of the FH-HETOP model to math proficiency data from the Early Childhood Longitudinal Study. Code for estimating the FH-HETOP model and conducting supporting calculations is provided in a new package for the R environment.

Suggested Citation

  • J. R. Lockwood & Katherine E. Castellano & Benjamin R. Shear, 2018. "Flexible Bayesian Models for Inferences From Coarsened, Group-Level Achievement Data," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 663-692, December.
  • Handle: RePEc:sae:jedbes:v:43:y:2018:i:6:p:663-692
    DOI: 10.3102/1076998618795124
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    References listed on IDEAS

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    1. Terrance Savitsky & Daniel McCaffrey, 2014. "Bayesian Hierarchical Multivariate Formulation with Factor Analysis for Nested Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 275-302, April.
    2. Gill, Jeff & Casella, George, 2009. "Nonparametric Priors for Ordinal Bayesian Social Science Models: Specification and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 453-454.
    3. Yuanyuan Gu & Denzil G. Fiebig & Edward Cripps & Robert Kohn, 2009. "Bayesian estimation of a random effects heteroscedastic probit model," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 324-339, July.
    4. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    5. Paddock, Susan M. & Ridgeway, Greg & Lin, Rongheng & Louis, Thomas A., 2006. "Flexible distributions for triple-goal estimates in two-stage hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3243-3262, July.
    6. Carol Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    7. Fienberg, Stephen E. & Holland, Paul W., 1972. "On the choice of flattening constants for estimating multinomial probabilities," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 127-134, March.
    8. Wei Shen & Thomas A. Louis, 1998. "Triple‐goal estimates in two‐stage hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 455-471.
    9. Sophia Rabe-Hesketh & Anders Skrondal, 2012. "Multilevel and Longitudinal Modeling Using Stata, 3rd Edition," Stata Press books, StataCorp LP, edition 3, number mimus2, March.
    10. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
    11. Bradley Efron, 2016. "Empirical Bayes deconvolution estimates," Biometrika, Biometrika Trust, vol. 103(1), pages 1-20.
    12. Susan M. Paddock & Thomas A. Louis, 2011. "Percentile‐based empirical distribution function estimates for performance evaluation of healthcare providers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(4), pages 575-589, August.
    13. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    14. Carol M. Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    15. Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 359-381, September.
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