Zero-one augmented beta and zero-inflated discrete models with heterogeneous dispersion for the analysis of student academic performance.

*(English)*Zbl 1437.62148Summary: 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/subjects. Three approaches are considered: first, the proportion of failed subjects is modeled considering a zero-one augmented beta distribution; second, discrete models are used to model the probability of failing subjects with logit link; third, incidence is modeled using regression for count data with log link and the logarithm of the total number of subjects as an offset. Zero-inflated versions are used to account for the excess of zeros in the data when appropriate and we also considered the heterogeneous dispersion parameter, when applicable. Overall, the zero-inflated negative binomial and zero inflated beta-binomial models, with regression on the mean and the dispersion parameters, present good measures of goodness of fit to the data. The database consists of records of Engineering major students who entered the State University of Campinas, Brazil, from 2000 to 2005. Entrance exam scores and demographic variables as well as socio-economic status are considered as covariates in the models.

##### MSC:

62G08 | Nonparametric regression and quantile regression |

62J12 | Generalized linear models (logistic models) |

62P25 | Applications of statistics to social sciences |

##### Keywords:

academic performance; heteroscedasticity; quantile residuals; residual analysis; overdispersion; zero-inflated discrete models; zero-one augmented beta models
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\textit{H. P. Pinheiro} et al., Stat. Methods Appl. 28, No. 4, 749--767 (2019; Zbl 1437.62148)

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