A model-based approach to measure school achievements in latent groups of students: a simulation study

In this paper, we present a model-based framework to estimate the educational attainments of students in latent groups defined by unobservable or only partially observed features which are likely to affect the outcome distribution, as well as being interesting to be investigated. We focus our attention on the case of students in the first year of the upper secondary schools, for which the teachers’ suggestion at the end of their lower educational level toward the subsequent type of school is available. We use this information to develop latent strata according to the compliance behavior of students simplifying to the case of binary data for both counselled and attended school (i.e., academic or technical institute). We consider a likelihood-based approach to estimate outcome distributions in the latent groups and propose a set of plausible assumptions with respect to the problem at hand. In order to assess our method and its robustness, we simulate data resembling a real study conducted on pupils of the province of Bologna in year 2007/2008 to investigate their success or failure at the end of the first school year.