Assessment of school evasion rates among undergraduate students using a discrete log-logistic regression model

Authors

DOI:

https://doi.org/10.5902/2179460X88599

Keywords:

Discrete log-logistics, Regression, Evasion, EMV

Abstract

School evasion, both in primary and secondary education, as well as in higher education, is certainly a problem that affects the results of the educational system in Brazil. In addition to being a problem that directly affects the country’s public spending, little is said about the subject and much less is there a policy to combat evasion. In search of some characteristics that explain the time until evasion occurs, one of the techniques that can be used is survival analysis. Traditionally, to model the time until the occurrence of an event of interest, continuous probability distributions are widely used. However, when this time is observed only in days, months or years, discrete probability distributions are more appropriate. To model and explain the dropout time of students in the Computer Science course at the Universidade Estadual da Paraíba – Campus I, we propose in this work the discrete Log-Logistic regression model. The parameters of the proposed model were estimated using the maximum likelihood method. To evaluate the accuracy of the estimators, the bias and mean squared error of the estimators are calculated using Monte Carlo simulation, considering different sample sizes and censoring percentages. From the estimated coefficients, it was found that age, the secondary education institution, the form of entry and the student’s study time on the course are factors that influence the time until your evasion.

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Author Biographies

Damião Flávio dos Santos, Universidade de Brasília

Bachelor's degree in Statistics from the Universidade Estadual da Paraíba (UEPB) and Master's degree in Statistics from the Universidade de Brasília (UnB).

Cira Etheowalda Guevara Otiniano, Universidade de Brasília

Bachelor's degree in Mathematics from the Universidad Nacional de Trujillo, Master's degree in Mathematics from the Universidade de Brasília (UnB), and PhD in Applied Mathematics from UnB.

Juliana Betini Fachini Gomes, Universidade de Brasília

Bachelor's degree in Statistics from the Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Master's degree in Agronomy and PhD in Sciences from the Universidade de São Paulo (USP).

References

ALDAHLAN, M.A. Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data. Advances in Mathematical Physics, v. 1, p. 1-9, 2020.

ASHKAR, F.; MAHDI, S. Fitting the log-logistic distribution by generalized moments. Journal of Hydrology, v. 328, n. 3, p. 694–703, 2006.

BENNETT, S. Log-Logistic Regression Models for Survival Data. Journal of the Royal Statistical Society. Series C (Applied Statistics), v. 32, n. 2, p. 165-171, 1983.

COLOSIMO, E. A.; GIOLO, S.R. Análise de Sobrevivência Aplicada. 2. ed. São Paulo: Blucher, 2024.

COLLET, D. Modelling Survival Data in Medical Research. London: Chapman and Hall, 2003.

FILHO, R. L. L. S.; MOTEJUNAS, P. R.; HIPÓLITO, O.; LOBO, M. B. C. M. A evasão no ensino superior brasileiro. Cadernos de Pesquisa, v. 37, p. 641-659, 2007.

FRITSCH, R.; ROCHA, C. S.; VITELLI, R. F. A evasão nos cursos de graduação em uma instituição de ensino superior privada. Educação em Questão, v. 52, n. 38, p. 81 – 108, 2015.

HASHEMIAN, A.H.; GARSHASBI, M.; POURHOSEINGHOLI, M.A.; ESKANDARI, S. A comparative study of cox regression vs. loglogistic regression (with and without its frailty) in estimating survival time of patients with colorectal cancer. Journal Medical Biomedical Sciences, v. 6, n. 1, p. 35–43, 2017.

HOSMER, D.; LEMESHOW, S. Applied Survival Analysis. New York: Wiley, 1999.

IBGE. Instituto Brasileiro de Geografia e Estatística. Censo Demográfico 2022. 2022. Disponível em: https://www.ibge.gov.br/estatisticas/sociais/trabalho/22827-censo-demografico-2022.html. Acesso em: 15 jun. 2024.

INEP. Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira. Sinopse Estatística da Educação Superior 2020. Brasília: Inep, 2022. Disponível em: https://www. gov.br/inep/pt-br/acesso-a-informacao/dados-abertos/sinopses-estatisticas/educacao-superior-graduacao. Acesso em: 15 jun. 2024.

KAPLAN, E. L.; MEIER, P. Nonparametric estimation from incomplete bservations. Journal of the American Statistical Association, v. 53, n. 282, p. 457–481, 1958.

KHALEEQA, J.; AMANULLAHA, M.; ABDULRAHMANB, A.T.; HAFEZC, E.; ABD EL-RAOUFD, H. Influence diagnostics in Log-Logistic regression model with censored data. Alexandria Engineering Journal, v. 61, n. 3, p. 2230-2241, 2022.

LAWLESS, J. F. Statistical Models and Methods for Lifetime Data. New York: John Wiley Sons, 2011.

LIMA JUNIOR, P.; SILVEIRA, F. L.; OSTERMANN, F. Survival analysis applied to student flow in undergraduate Physics courses: an example from a Brazilian university. Revista Brasileira de Ensino de Física, v. 34, n. 1, p. 1-10, 2012.

LIMA, J. G. Modelo de regressão log-logístico discreto para dados da política de zoneamento e uso do solo na presença de observações censuradas. 2018. Trabalho de conclusão de curso (Bacharelado em Estatística) - Universidade de Brasília, Brasília, 2018.

LOUZADA-NETO, F.; PEREIRA, B. Modelos em análise de sobrevivência. Cadernos Saúde Coletiva, Rio de Janeiro, v. 8, n. 1, p. 8–26, 2000.

NAKAGAWA, T.; OSAKI, S. The discrete weibull distribution. IEEE Transactions on Reliability, v.24, n.5, 300–301, 1975.

NAKANO, E. Y.; CARRASCO, C. G. Uma avaliação do uso de um modelo contínuo na análise de dados discretos de sobrevivência. Trends Computational and applied mathematics, v. 7, n.1, p. 91-100, 2006.

ROSA, C. M. Limites da democratização da educação superior: Entraves na permanência e a evasão na universidade federal de Goiás. Revista Poíesis Pedagógica, v. 37, p. 641 – 659, 2007.

R CORE TEAM, R. et al. R: A language and environment for statistical computing.

Vienna: Statistical Computing, Vienna, Austria, 2025.

SANTOS, D. F. Modelo de regressão log-logístico discreto com fração de cura para dados de sobrevivência. 2017. 81 f. Dissertação (Mestrado em Estatística) - Universidade de Brasília, Brasília, 2017.

SEMESP. Mapa do Ensino Superior. 2022. Disponível em: https://www.semesp.org.br/mapa/edicao-12/. Acesso em: 15 jun. 2024.

TAHIR, M.H.; MANSOOR,M.; ZUBAIR, M.; HAMEDANI, G. Mcdonald Log-logistic distribution with an application to breast cancer data. Mathematics, Statistics and Computer Science Faculty Research and Publications, v. 13, n. 1, p. 65-82, 2014.

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Published

2026-07-01