Published

2017-09-01

Value-added in higher education: ordinary least squares and quantile regression for a Colombian case

Valor agregado en educación superior: mínimos cuadrados ordinarios y regresión cuantílica para un caso colombiano

Keywords:

Value-added, higher education, evaluation, quantile regression, statistical model. (en)
Valor agregado, educación superior, evaluación, regresión cuantílica, modelo estadístico. (es)

Downloads

Authors

  • Jose D Bogoya Independent Consultant
  • Johan M Bogoya Universidad Javeriana
  • Alfonso J Peñuela Universidad Sergio Arboleda

Colombia applies two mandatory National State tests every year. The first, known as Saber 11, is applied to students who finish the high school cycle, whereas the second, called Saber Pro, is applied to students who finish the higher education cycle. The result obtained by a student on the Saber 11 exam along with his/her gender, and socioeconomic stratum are our independent variables while the Saber Pro outcome is our dependent variable.

We compare the results of two statistical models for the Saber Pro exam. The first model, multi-lineal regression or ordinary least squares (OLS), produces an overall well fitted result but is highly inaccurate for some students. The second model, quantile regression (QR), weight the population according to their quantile groups. OLS minimizes the errors for the students whose Saber Pro result is close to the mean (a process known as estimation in the mean) while QR can estimate in the -quantile for every . We show that QR is more accurate than OLS and reveal the unknown behavior of the socioeconomic stratum, the gender, and the initial academic endowments (estimated by the Saber 11 exam) for each quantile group.

En el sistema educativo de Colombia se realizan dos exámenes nacionales obligatorios al año. El primero, conocido como Saber 11, está dirigido a los estudiantes que finalizan el bachillerato, mientras que el segundo, conocido como Saber Pro, evalúa a los estudiantes que terminan un estudio superior. En este estudio, el resultado obtenido por un estudiante en el examen Saber 11, junto con su género y estrato socioeconómico, son nuestras variables independientes, mientras que el resultado del examen Saber Pro es nuestra variable dependiente.

Comparamos los resultados de dos modelos estadísticos para Saber Pro. El primer modelo, regresión multi-lineal o mínimos cuadrados (OLS, por sus siglas en inglés), produce un buen ajuste general pero es impreciso para ciertos estudiantes. El segundo modelo, regresión cuantílica (QR, por sus siglas en inglés), mide la población de acuerdo con su cuantil. El OLS minimiza los errores para los estudiantes cuyo resultado en Saber Pro está cercano a la media (proceso conocido como estimación en la media) mientras que el QR puede estimar un valor en el cuantil θ para cada 0 < θ < 1. Mostraremos que el QR es más preciso que el OLS y revelaremos el comportamiento desconocido del estrato socio económico, el género y la preparación académica inicial (estimada con el examen Saber 11) para cada cuantil.

References

Amrein-Beardsley, A. (2008). Methodological concerns about the education value-added assessment system. American Educational Researcher, 37(2), 65-75.

Bishop, J. H. & Woessmann, L. (2004). Institutional effects in a simple model of educational production. Cornell University ILR School.

Bogoya, J. D. & Bogoya, J. M. (2013). An academic valueadded mathematical model for higher education in Colombia. Ingeniería e Investigación, 33(2), 76-81.

Brennan, A., Cross, P.C., & Creel, S. (2015). Managing more than the mean: using quantile regression to identify factors related to large elk groups. Journal of Applied Ecology, 52(6), 1656-1664.

Cameron, A. C. & Trivedi, P. K. (2010). Microeconometrics using Stata. Stata Press, Texas 2010.

Frumento, P. & Bottai, M. (2016). Parametric modelling of quantile regression coefficient functions. Biometrics, 72(1), 74-84.

Hanushek, E. A. (1979). Conceptual and empirical issues in the estimation of educational production functions. The Journal of Human Resources, 14(3), 351-388.

Hanushek, E. A., Jackson, J. E., & Kain J. F. (1974). Model specification, use of aggregate data, and the ecological correlation fallacy. Political Methodology, 1(1), 89-107.

Hanushek, E. A. & Raymond, M. E. (2001). The confusing world of educational accountability. National Tax Journal, 54(2), 365-384.

Hanushek, E. A. & Rivkin, S. G. (2012). The distribution of the teacher quality and implications for policy. Annual Review of Economics, 4, 131-157.

Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91, 74-89.

Koenker, R. & Bassett, G. (1978). Regression quantiles. Econome trica, 46(1), 33-50.

Koenker, R. & Machado, J. A. F. (1999). Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association, 94(448), 1296- 1310.

Koenker, R. & Hallock, K. (2001). Quantile regression. Journal of Econometrics Perspectives, 15(4), 143-156.

Ray, A. (2006). School value added measures in England. A paper for the OECD Project on the development of valueadded models in educations systems.

Tymms, P. & Dean, C. (2004). Value-added in the primary school league tables. A report for the National Association of the Head Teachers.

Woessmann, L. (2004). How equal are educational opportunities? Family background and student achievement in Europe and the US. CESIFO Working Paper No. 1162.

License

Copyright (c) 2017 Jose D Bogoya, Johan M Bogoya, Alfonso J Peñuela

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:

1.    The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;

2.    The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;

3.    The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;

4.    The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.