Statistical modelling of gained university credits to evaluate the role of pre-enrolment assessment tests: An approach based on quantile regression for counts

Considering the case of the School of Economics of the University of Florence, the paper investigates whether the pre-enrolment assessment test is an effective tool to predict student performance. The analysis is tailored to evaluate the additional information yielded by the test beyond the background characteristics of the candidates already available from administrative records, such as the high school type and final grade. The student performance is measured by the number of gained credits after one year, which is a count variable with an irregular distribution and a peak in zero. These features pose a challenge in statistical modelling, which is solved by a two-part model with a logit specification for the zeros, while positive values are analyzed by quantile regression for counts. To disentangle direct and indirect effects of background variables, the result of the pre-enrolment assessment test is treated as an intermediate variable in a regression chain graph. The results show that the pre-enrolment test adds some information to predict student performance, which can be exploited for tutoring.