Linear and nonlinear growth models for value-added assessment: an application to Spanish primary and secondary schools’ progress in reading comprehension Esther Lopez-Martin & Timo Kuosmanen & Jose Luis Gaviria Received: 9 March 2013 /Accepted: 24 February 2014 / Published online: 13 March 2014 # Springer Science+Business Media New York 2014 Abstract Value-added models are considered one of the best alternatives not only for accountability purposes but also to improve the school system itself. The estimates provided by these models measure the contribution of schools to students’ academic progress, once the effect of other factors outside school control are eliminated. The functional form for the growth of students’ performance is a key aspect to be consid- ered when calculating value-added estimations, and, in this regard, there are several reasons that might suggest a nonlinear growth trajectory over time. This aspect is especially important when a variable such as reading comprehension is analyzed, since this is a skill in which nonlinear progression can be expected. This paper focuses on this issue and proposes to estimate schools’ value-added under nonlinear growth models where changes in performance follows a quadratic trajectory, analyzing differences in results with respect to those provided by linear growth models. To illustrate this point, the value-added in reading comprehension was estimated for three parallel cohorts that collect data from 153 primary and secondary schools in Madrid (Spain) and 6,755 students who were assessed at four different times during the academic years 2005– Educ Asse Eval Acc (2014) 26:361–391 DOI 10.1007/s11092-014-9194-1 E. Lopez-Martin Department: Research Methods and Diagnosis in Education II, National University of Distance Education, Madrid, Spain T. Kuosmanen Department: Quantitative Methods, Aalto University School of Economics, Helsinki, Finland e-mail: timo.kuosmanen@aalto.fi J. L. Gaviria Department: Research Methods and Diagnosis in Education, Complutense University of Madrid, Madrid, Spain e-mail: josecho@edu.ucm.es E. Lopez-Martin (*) Department MIDE II, Universidad Nacional de Educación a Distancia, C/ Juan del Rosal, no. 14, C.P. 28040 Madrid, Spain e-mail: estherlopez@edu.uned.es