Modeling of Distance Learners’ Retention Using Mixed-Model on Non-Proportional Hazard




Universitas Terbuka, distance learners’ retention, analysis survival, mixed-model on the non-proportional hazard


Universitas Terbuka is a public university in Indonesia that implements an open-distance education system. The quality and success of higher education in Indonesia are indicated by the gross enrolment rate (GER). Modelling student retention is one indicator of the value of the GER. The chances of distance learners’ retention in a certain period can be determined through survival analysis, namely the “Cox model” or “Cox proportional hazard model”. The limitations of the Cox model pose new problems in modelling that involve more than two types of covariates and the presence of random effects. The problem that arises is the non-proportional hazard. The cause of non-proportional hazard is time-dependent covariates, so that individual risk changes over time. Another reason is the presence of random effects, both observed and unobserved. In this model, there are two random effects, namely, the unobserved random effect and the observed random effect. Thus, the model is called the mixed effect model of non-proportional hazard. Based on the characteristics of the covariates observed, appropriate survival analysis for modelling distance learners’ retention is a mixed model on the non-proportional hazard. The covariates involved in very complex modelling include time-independent covariates, time-dependent covariates, and unobserved random effects. The results of the analysis with the mixed model on non-proportional hazard showed that the covariates that significantly affected the distance learner’s retention were: educational background, age, grade point average, marital status, scholarship, independent learning culture, number of credits taken, and number of courses taken each semester.

Author Biography

Dewi Juliah Ratnaningsih, Universitas Terbuka

Dewi Juliah Ratnaningsih is an Associate Professor of the Faculty of Science and Technology at Universitas Terbuka (UT). Her academic interest areas are statistics, applied statistics in education, studies of services, customer satisfaction, tracer study, developing research instruments, open and distance learning, and needs assessment for distance education. She has had seven articles published in international indexes and Scopus indexed (Asian Association of Open Universities Journal, Turkish Online Journal of Distance Education, Journal of Applied Statistics, Journal of the Indonesian Mathematical Society, Thailand Statistician, and IOP conference Series: Earth and Environment Science. She was awarded First Prize in Excellent Paper Winner of the 25th International Council for Open and Distance Education (ICDE) World Conference, and ICDE Prizes for Innovation and Best Practice (2013). She has published six books on statistics.

Porait of Dewi Ratnaningsih