Zero-one Augmented Beta and Zero Inflated Discrete Models with Heterogeneous Dispersion: An Application to Students’ Academic Performance

Hildete P. Pinheiro
Rafael P. Maia
Eufrásio A. Lima-Neto
Mariana Rodrigues-Motta

The purpose of this work is to present suitable statistical methods to study the performance of undergraduate students based on the incidence/proportion of failed courses. Some approaches are considered: in one of them the incidence of failed courses is modeled using zero in ated discrete distributions with heteroscedasticity, considering
the logarithm of the total number of courses as an o set; in another, the proportion of failed courses is modeled considering a zero-one augmented
beta distribution with heterogeneous dispersion parameter. A detailed residual analysis is performed to investigate the best model to  t the data. The zero-one augmented beta model with heteroscedasticity presents a better t based on residual analysis. Moreover, the model for the proportion brings us more information as it is straight
forward to interpret its results. The database consists of records of 3,699 students with Engineering major who entered the State University of Campinas, Brazil, from 2000 to 2005. The entrance exam scores, academic and demographic variables and their socioeconomic status are considered as covariates in the models.

Academic performance Heteroscedasticity Quantile residuals Residual anal