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

Abstract

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.