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Temporally Dynamic, Cohort-Varying Value-Added Models

Author

Listed:
  • Garritt L. Page

    (Brigham Young University)

  • Ernesto San Martín

    (MILLENNIUM NUCLEUS ON INTERGENERATIONAL MOBILITY MOVI
    LIDAM/CORE, Université catholique de Louvain
    Pontificia Universidad Católica de Chile)

  • David Torres Irribarra

    (School of Psychology, Pontificia Universidad Católica de Chile)

  • Sébastien Van Bellegem

    (LIDAM/CORE, Université catholique de Louvain)

Abstract

We aim to estimate school value-added dynamically in time. Our principal motivation for doing so is to establish school effectiveness persistence while taking into account the temporal dependence that typically exists in school performance from one year to the next. We propose two methods of incorporating temporal dependence in value-added models. In the first we model the random school effects that are commonly present in value-added models with an auto-regressive process. In the second approach, we incorporate dependence in value-added estimators by modeling the performance of one cohort based on the previous cohort’s performance. An identification analysis allows us to make explicit the meaning of the corresponding value-added indicators: based on these meanings, we show that each model is useful for monitoring specific aspects of school persistence. Furthermore, we carefully detail how value-added can be estimated over time. We show through simulations that ignoring temporal dependence when it exists results in diminished efficiency in value-added estimation while incorporating it results in improved estimation (even when temporal dependence is weak). Finally, we illustrate the methodology by considering two cohorts from Chile’s national standardized test in mathematics.

Suggested Citation

  • Garritt L. Page & Ernesto San Martín & David Torres Irribarra & Sébastien Van Bellegem, 2024. "Temporally Dynamic, Cohort-Varying Value-Added Models," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 1074-1103, September.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:3:d:10.1007_s11336-024-09979-0
    DOI: 10.1007/s11336-024-09979-0
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