Issues in prior achievement adjustment for value added analysis: an application to Invalsi tests in Italian schools

We consider the issue of estimating the effect of schools on student achievement when a pre- test is available. Based on Invalsi data (Martini, 2018), our focus is on the value added of the lower secondary schools on test scores at the 8th grade (post-test), accounting for the student test scores at the 5th grade (pre-test), and controlling for the available student and school char- acteristics by multilevel models (Goldstein, 2010). In this framework, the school value added can be estimated by either inserting the pre-test score as a covariate (conditioning approach), or by considering the difference between post-test and pre-test scores as the response (gain score approach). We discuss the assumptions underlying each approach (Kim and Steiner, 2019), and the consequences of their violations, and we present a comparison of the results obtained with the two approaches on Invalsi data.