Thesis (M. Sc. (Statistics)) -- University of Limpopo, 2021 / The ever increasing number of students who drop out of university remains a challenge for Higher Education administrators. In response to this, different studies have been conducted globally in order to identify student retention strategies to fix the problem. However, the challenge continues to prevail year in and year out. Most of the studies conducted in South Africa used statistical methods that ignore the temporal nature of the process of student dropout. This study uses discrete-time survival techniques to model the occurrence and timing of undergraduate engineering student dropout at Tshwane University of Technology (TUT). Discrete-time survival analysis techniques allow for a more appropriate utilisation of the longitudinal nature of institutional data, where the time dependence of the data, time-varying factors and time-invariant factors can all be accommodated in the analysis. The temporal nature of the process of student dropout was analysed for the cohort of students registered in engineering programmes for the first time in 2010 at Tshwane University of Technology using discrete-time survival analysis methods. The cohort was followed for five years from 2010 through 2014, inclusive. Of particular interest was the incidence of dropout, the determinants of dropout, comparison of the single risk discrete-time model with a competing risk discrete-time model, as well as testing for the effects of unobserved heterogeneity. The study used administrative data obtained from the ITS. The logit model was used to estimate the effects of race, gender, Matric performance, performance in Matric Mathematics, residence type, English language status and time on time to dropout with time measured in academic years. A discretetime competing risk model in the form of a multinomial logit model was also estimated to account for the possible correlation between graduation and dropout. A frailty model assuming a Gaussian distribution for the frailty term was also estimated to account for unobserved heterogeneity. The study established that the risk of dropout for nonwhite students is significantly higher than that of white students. Furthermore, it was found that the effects of residence type varied with time. For instance, in the first year students with private based accommodation were more likely to dropout compared to those residing onvi Abstract campus. On the other hand, in the third year students accommodated in private residences were less likely to dropout than those residing on-campus. The findings also indicate that the effect of having English as a first language as opposed to as a second language on the risk of dropout was only significant in the fourth year such that first language English students were more at risk of dropout compared to second language students. The findings also revealed inconsistencies between the estimates from the single risk and the competing risk model. Moreover, the effect of unobserved heterogeneity was found to be insignificant. Recommendations from this study are that discrete-time survival analysis model is more efficient than traditional methods used for analysis of student dropout and should therefore be used for analysis of academic outcomes such as dropout. The model can account for the temporal nature of the process of dropout. Both time-varying and time-invariant explanatory variables can be included in the model.The effects of time-invariant explanatory variables that might have time-varying effects can also be investigated.