An association model for bivariate data with application to the analysis of university students' success

Abstract

The academic success of students is a priority for all universities. We analyze the students' success at university by considering their performance in terms of both ‘qualitative performance’, measured by their mean grade, and ‘quantitative performance’, measured by university credits accumulated. These data come from an Italian University and concern a cohort of students enrolled at the Faculty of Economics. To jointly model both the marginal relationships and the association structure with covariates, we fit a bivariate ordered logistic model by penalized maximum likelihood estimation. The penalty term we use allows us to smooth the association structure and enlarge the range of possible parameterizations beyond that provided by the usual Dale model. The advantages of our approach are also in terms of parsimony and parameter interpretation, while preserving the goodness of fit.

Keywords:

• bivariate ordinal response
• Dale's model
• maximum penalized likelihood estimation
• models for association
• students' performance

Acknowledgments

We are very grateful to the two anonymous referees for their constructive comments. A special thank goes to Sandra for the English revision. The authors contributed to write this manuscript in the following way. The first author proposed the methodology, developed the R codes, and carried out the analyses. He wrote Sections 2–4 and contributed to write Sections 1 and 5. The second author proposed the application, supervised the writing of the article, and contributed to write Sections 1 and 5.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Ministero dell'Istruzione, dell'Universitá e della Ricerca (MIUR), PRIN 2008 ‘Measures, statistical models and indicators for the assessment of the University System’ [grant n. 2008WXSLH].