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Contrasting OLS and Quantile Regression Approaches to Student “Growth†Percentiles

Author

Listed:
  • Katherine Elizabeth Castellano

    (University of Iowa)

  • Andrew Dean Ho

    (Harvard Graduate School of Education)

Abstract

Regression methods can locate student test scores in a conditional distribution, given past scores. This article contrasts and clarifies two approaches to describing these locations in terms of readily interpretable percentile ranks or “conditional status percentile ranks.†The first is Betebenner’s quantile regression approach that results in “Student Growth Percentiles.†The second is an ordinary least squares (OLS) regression approach that involves expressing OLS regression residuals as percentile ranks. The study describes the empirical and conceptual similarity of the two metrics in simulated and real-data scenarios. The metrics contrast in their scale-transformation invariance and sample size requirements but are comparable in their dependence on the number of prior years used as conditioning variables. These results support guidelines for selecting the model that best fits the data and have implications for the interpretations of these percentiles ranks as “growth†measures.

Suggested Citation

  • Katherine Elizabeth Castellano & Andrew Dean Ho, 2013. "Contrasting OLS and Quantile Regression Approaches to Student “Growth†Percentiles," Journal of Educational and Behavioral Statistics, , vol. 38(2), pages 190-215, April.
  • Handle: RePEc:sae:jedbes:v:38:y:2013:i:2:p:190-215
    DOI: 10.3102/1076998611435413
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    References listed on IDEAS

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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Holger Dette & Stanislav Volgushev, 2008. "Non‐crossing non‐parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627, July.
    3. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
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    Cited by:

    1. Bernard, Carole & Czado, Claudia, 2015. "Conditional quantiles and tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 104-126.

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