Modelling time to graduation of Durban University of Technology students using event history analysis.

Abstract

Tertiary institutions experienced a steady growth of students from other races after the repeal of the apartheid laws. This growth picked up pace after the promulgation of the Education White Paper of 1997 whose main thrust was to make the previously exclusive institutions accessible to the wider populace. Disturbingly, however, and contrary to the goals and the spirit of the White Paper, these institutions also experienced higher failure and lower retention rates amongst the previously disadvantaged students. This study seeks to model time to graduation using survival analysis methods. We begin the analysis by assessing the relevance of the available variables to the exercise of modelling time to graduation using descriptive statistics and non-parametric techniques. We compared the Cox regression to its extensions in discrete time, the Discrete Time to Event Approach, with the view to find the best model to explain time to graduation given the available variables. In light of limited availability of relevant data, we evaluated unobserved heterogeneity in both models. We closed the analysis by considering the cure models and mixture competing risks in discrete time. Notwithstanding arguments against suitability of the Cox regression in continuous time for modelling inherently discrete data such as found in our study, we found that Cox's regression over all, provided a reasonably good fit given the available data. We also found that in relation to the Cox proportional hazard model, there was a lesser degree of exibility as certain variable effects were sacrificed to satisfy the proportionality assumption by stratifying on those variables. The advantage of the Discrete Time to Event Approach is that we could assess the effects of all variables in the model and also obtain the estimates of risks to graduation which are true probabilities of graduation with fewer assumptions or conditions to satisfy. We found that the data limitations did not compromise either the box Cox regression model or the Discrete Time to Event Approach. The data also suggested existence of a sizable proportion of subjects that will eventually not graduate based on cure models. We also fractionated subjects censored due to closure of the observation period into those that will eventually graduate and those that will eventually dropout, using discrete mixture competing risks. We found that the mixture competing risks model explained graduation better than the cure model.