Advertisement

Social Indicators Research

, Volume 146, Issue 1–2, pp 7–18 | Cite as

Concomitant-Variable Latent-Class Beta Inflated Models to Assess Students’ Performance: An Italian Case Study

  • Marco Centoni
  • Vieri Del Panta
  • Antonello MaruottiEmail author
  • Valentina Raponi
Article
  • 75 Downloads

Abstract

Students’ performance is a crucial aspect for university programs effectiveness and organization. In this paper, we introduce and analyze a performance index for the first-year students of a private Italian university, namely the Libera Università Maria Ss. Assunta. We use administrative data on 532 undergraduate students enrolled in any of the eight available bachelor degrees in 2015. Our aim is to improve the general understanding of performance linking it with personal student’s characteristics and with degree-specific aspects. A beta inflated latent class approach is employed to identify clusters of performance establishing a link with all available explanatory variables. The empirical analysis unveils that a good and balanced degree organization may improve students’ performance. The student’s ability plays a crucial role in discriminating between good and bad performances, and also strongly depends on individual-specific characteristics, such as the final mark obtained at high school.

Keywords

Latent class Students’ performance Private university Beta distribution Zero-inflation 

References

  1. Adelfio, G., & Boscaino, G. (2016). Degree course change and student performance: A mixed-effect model approach. Journal of Applied Statistics, 43(1), 3–15.CrossRefGoogle Scholar
  2. Bagnato, L., & Punzo, A. (2013). Finite mixtures of unimodal beta and gamma densities and the \(k\)-bumps algorithm. Computational Statistics, 28(4), 1571–1597.CrossRefGoogle Scholar
  3. Belloc, F., Maruotti, A., & Petrella, L. (2010). University drop-out: An Italian experience. Higher Education, 60(2), 127–138.CrossRefGoogle Scholar
  4. Belloc, F., Maruotti, A., & Petrella, L. (2011). How individual characteristics affect university students drop-out: A semiparametric mixed-effects model for an Italian case study. Journal of Applied Statistics, 38(10), 2225–2239.CrossRefGoogle Scholar
  5. Bini, M., Bertaccini, B., & Bacci, S. (2009). Robust diagnostics in university performance studies (pp. 139–160). Heidelberg: Physica-Verlag HD.Google Scholar
  6. Cao, Z., & Maloney, T. (2017). Decomposing ethnic differences in university academic achievement in New Zealand. Higher Education,.  https://doi.org/10.1007/s10734-017-0157-6.CrossRefGoogle Scholar
  7. Dayton, C. M., & Macready, G. B. (1988). Concomitant-variable latent-class models. Journal of the American Statistical Association, 83(401), 173–178.CrossRefGoogle Scholar
  8. Dehbi, H. M., Cortina-Borja, M., & Geraci, M. (2016). Aranda-Ordaz quantile regression for student performance assessment. Journal of Applied Statistics, 43(1), 58–71.CrossRefGoogle Scholar
  9. Enea, M., & Attanasio, M. (2016). An association model for bivariate data with application to the analysis of university students’ success. Journal of Applied Statistics, 43(1), 46–57.CrossRefGoogle Scholar
  10. Gnaldi, M., & Ranalli, M. G. (2016). Measuring university performance by means of composite indicators: A robustness analysis of the composite measure used for the benchmark of Italian universities. Social Indicators Research, 129(2), 659–675.CrossRefGoogle Scholar
  11. Grilli, L., Rampichini, C., & Varriale, R. (2015). Binomial mixture modeling of university credits. Communications in Statistics - Theory and Methods, 44(22), 4866–4879.CrossRefGoogle Scholar
  12. Grilli, L., Rampichini, C., & Varriale, R. (2016). Statistical modelling of gained university credits to evaluate the role of pre-enrolment assessment tests: An approach based on quantile regression for counts. Statistical Modelling, 16(1), 47–66.CrossRefGoogle Scholar
  13. Johnes, J. (1990). Determinants of student wastage in higher education. Studies in Higher Education, 15(1), 87–99.CrossRefGoogle Scholar
  14. Johnson, N. L., & Kotz, S. (1970). Continuous univariate distributions (Vol. 2). Hoboken: Wiley.Google Scholar
  15. Maia, R. P., Pinheiro, H. P., & Pinheiro, A. (2016). Academic performance of students from entrance to graduation via quasi U-statistics: A study at a Brazilian research university. Journal of Applied Statistics, 43(1), 72–86.CrossRefGoogle Scholar
  16. McLachlan, G., & Krishnan, T. (2007). The EM algorithm and extensions (Vol. 382). Hoboken: Wiley.Google Scholar
  17. Meggiolaro, S., Giraldo, A., & Clerici, R. (2017). A multilevel competing risks model for analysis of university students careers in Italy. Studies in Higher Education, 42(7), 1259–1274.CrossRefGoogle Scholar
  18. Meng, X. L., & Rubin, D. B. (1994). On the global and component-wise rates of convergence of the EM algorithm. Linear Algebra and its Applications, 199, 413–425.CrossRefGoogle Scholar
  19. Ospina, R., & Ferrari, S. L. (2012). A general class of zero-or-one inflated beta regression models. Computational Statistics & Data Analysis, 56(6), 1609–1623.CrossRefGoogle Scholar
  20. Ospina, R., & Ferrari, S. L. P. (2008). Inflated beta distributions. Statistical Papers, 51(1), 111.CrossRefGoogle Scholar
  21. Raponi, V., Martella, F., & Maruotti, A. (2016). A biclustering approach to university performances: An Italian case study. Journal of Applied Statistics, 43(1), 31–45.CrossRefGoogle Scholar
  22. Redner, R. A., & Walker, H. F. (1984). Mixture densities, maximum likelihood and the EM algorithm. SIAM Review, 26(2), 195–239.CrossRefGoogle Scholar
  23. Rienties, B., Beausaert, S., Grohnert, T., Niemantsverdriet, S., & Kommers, P. (2012). Understanding academic performance of international students: The role of ethnicity, academic and social integration. Higher Education, 63(6), 685–700.CrossRefGoogle Scholar
  24. Smith, J. P., & Naylor, R. A. (2001). Dropping out of university: A statistical analysis of the probability of withdrawal for UK university students. Journal of the Royal Statistical Society: Series A (Statistics in Society), 164(2), 389–405.CrossRefGoogle Scholar
  25. van der Heijden, P. G. M., Dessens, J., & Bockenholt, U. (1996). Estimating the concomitant-variable latent-class model with the EM algorithm. Journal of Educational and Behavioral Statistics, 21(3), 215–229.CrossRefGoogle Scholar
  26. Wu, C. J. (1983). On the convergence properties of the EM algorithm. The Annals of Statistics, 11, 95–103.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Giurisprudenza, Economia, Politica e Lingue ModerneLibera Università Maria Ss. AssuntaRomeItaly
  2. 2.Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza (MEMOTEF)Sapienza Università di RomaRomeItaly
  3. 3.Imperial College Business SchoolImperial CollegeLondonUK

Personalised recommendations