Value-added models are a set of complex statistical techniques that use data from students’ test scores throughout several years to estimate the effects of schools individually. The models pursue to isolate the contributions of these to student learning development (Martinez et al., 2009). The numerical estimates provided a separation of school effects on student learning in a better way than other methods do (Martinez Arias, 2009). These models, and, by extension, growth models, calculate the increase as the difference between two or more points over time. The point of departure corresponds with the initial performance and the point of arrival is the final performance. In practice, different approaches to calculate the distance in performance between these temporal points have produced varied models to evaluate the value-added factor. These models range from the simplest value added models, in which previous scores are subtracted from current scores to obtain a gain, to another model that requires more complex assumptions (Sanders, 2006).

Diverse illustrations of value-added models can be found in the literature (Tekwe et al. 2004; Sander, 2006; Shin, 2007; OECD, 2008) and the main difference between them is how to quantify the growth. The choice among methods depends on their characteristics and properties. All of them require longitudinal data; however, other assumptions can affect the choice of the method, such as the numerical scale of scores, the form of growth function or the question to be answered.

In this paper, Multilevel Models have been applied to calculate value-added measurements with the purpose of respecting the hierarchical nature of educational data, analyzing the functional form that best represents the performance growth for the sample evaluated and estimating the effect of schools over the student development. This method is presented as the most appropriate methodological alternative to calculate value-added measures because the nested nature of the educational data is respected, recognizing expressly different sources of variability (Martinez Arias et al. 2009, Martinez Arias, 2009). Similarly, multilevel models require a common scale so that it is reasonable to compute the difference between two moments because the two scores have the same meaning (Reckase, 2004). Finally, although a majority of the methods provide a linear growth measurement, that growth over many years could be curved (Reckase, 2004; CCSSO, 2008), and for this reason multilevel models allow assessing linear and non-linear growth. 

The present study emerges from the interest in finding a measure that quantifies the schools contribution to their students’ reading skill. In this way, the main aim will be to calculate the value added in reading comprehension throughout compulsory education, applying the hierarchical linear models.

This general aim is made up of more specific points: To modelize the growth in reading comprehension of the schools that make up the sample; to analyze the existing relation between the schools initial performance and their growth rates in the course of time; and to compare the growth functional form in reading comprehension along the different stages that compose the compulsory education. 

CCSSO. (2008). Implementer’s Guide to Growth Models: A paper commissioned by the CCSSO Accountability Systems and Reporting State Collaborative on Assessment and Student Standards. Washington, DC: The Council of Chief State School Officers. Martinez Arias, R. (2009). Usos, aplicaciones y problemas de los Modelos de Valor Añadido en Educación. In Revista de Educación, 348 (1), pp. 217-250. Martinez Arias, R., Gaviria Soto, J.L. y Castro Morera, M. (2009) Concepto y Evolución de los Modelos de Valor Añadido en Educación. In Revista de Educación, 348 (1), pp. 15-45. OECD (2008). Measuring Improvements in Learning Outcomes. Best Practices to Assess the Value-Added of Schools. Paris: OECD Publishing. Reckase, M. D. (2004). The Real World is More Complicated than We Would like. In Journal of Educational and Behavioral Statistics, 29 (1), pp. 117-120. Sanders, W.L. (2006). Comparisons among various educational assessment value-added models. Paper presented at The Power of Two-National Valued-Added Conference, October 16, 2006, Columbus, Ohio. Shin, T. (2007). Comparison of Thee Growth Modeling Techniques in the Multilevel Analysis of Longitudinal Academic Achievement Scores: Latent Growth Modeling, Hierarchical Linear Modeling, and Longitudinal Profile Analysis via Multidimensional Scaling. In Asia Pacific Education Review, 8 (2), pp. 262-275. Tekwe, C.D.; Carter, R. L.; Ma, C-X; Algina, J.; Lucas, M. E.; Roth, J.; Ariet, M.; Fisher, T. & Resnick, M. B. (2004) An Empirical Comparison of Statistical Models for Value-Added Assessment of School Performance. In Journal of Educational and Behavioral Statistics, 29 (1), pp. 11-35.