Title: Adjusting for a pre-test in school value-added models: A comparison between gain score and conditional approaches
Authors: Carla Rampichini - University of Florence (Italy) [presenting]
Bruno Arpino - Department of Statistics Computer Science Applications University of Florence (Italy)
Silvia Bacci - Department of Statistics Computer Science Applications University of Florence (Italy)
Leonardo Grilli - University of Florence (Italy)
Raffaele Guetto - Department of Statistics Computer Science Applications University of Florence (Italy)
Abstract: The issue of prior achievement adjustment in value added models is considered. Based on data of the National Institute for the Evaluation of the Education System in Italy (INVALSI), our focus is on the effect of the lower secondary school type (public versus private) on test scores at the 8th grade (post-test), accounting for students test scores at the 5th grade (pre-test). Such effect can be estimated by either adjusting for the pre-test score (i.e. conditioning) or by using the difference between post-test and pre-test scores (gain score) as response variable. We discuss the assumptions underlying the gain score approach as compared to the conditional approach, and the consequences of their violations. We evaluate the two approaches by means of an application using INVALSI data and by a simulation study that explicitly takes into account the multilevel structure of the data. The results show that the performance of the two approaches, in terms of bias and efficiency, depends on several factors, such as pre-test reliability and validity of the common trend assumption.