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March 21, 2022
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December 7, 2022
Published
December 10, 2022
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Abstract

The problem that arises in the Cox model is that there are more than two types of covariates and the presence of random effects is a non-proportional hazard (NPH). One example of a case that involves many factors is student retention. Low student retention can lead to dropping out of college or failure in completing studies. The purpose of this study is to overcome the problem of NPH caused by the presence
of time-independent covariates, time-dependent covariates, and random effects. The research method uses simulation. Some of the modified models are the stratified Cox model, the extended Cox model, and the frailty model. The developed model is applied to distance education student retention data. The results of the study show that frailty and study programs provide considerable diversity in explaining the
total diversity of the model. It can be concluded that frailty needs to be considered by UT to improve the quality of services to students. In addition, other covariates that have a significant effect on UT student learning retention modeling are age, domicile, gender, GPA, marital status, employment status, number of credits taken, and number of registered courses.

Keywords

Universitas Terbuka stratified Cox extended Cox frailty mixed effect model

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Author Biographies

Dewi Juliah Ratnaningsih, Universitas Terbuka

DEWI JULIAH RATNANINGSIH is an Associate Professor of Faculty of Mathematics and Natural Sciences at Universitas Terbuka (UT). Her academic interest areas are statistics, applied statistics in education, studies of services, customer satisfaction, tracer study, developing research instrument, open and distance learning and needs assessment for distance education.  She has three articles that have been published in international indexes and scopus indexed (Asian Association of Open Universities Journal, Open Praxis, and Journal of Applied Statistics).  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 five books on statistics.

Anang Kurnia, IPB University

ANANG KURNIA is an Assosiate Professor of Departemen of Statistics,  Faculty of Mathematics and Natural Sciences at Bogor Agricultural University. His research interests include: small area estimation, generalized linear (mixed) model, robust statistics, and high-dimensional data analysis. He is head of Department of Statistics in Bogor Agricultural University and former head of Indonesian Statistics Higher Education Association.  He has published any journal and conference papers and also coordinated some researches project in statistics.

Asep Saefuddin, IPB University

ASEP SAEFUDDIN is Professor of Departemen of Statistics at Bogor Agricultural University. He obtained a master's and doctorate degrees in Biostatistics and Populations Medicine/ Quantitative Epidemiology from the University of Guelph. He served as Vice Rector for Planning, Development and Cooperation, Bogor Agricultural University in 2003-2008. Year 2013-2017 as Rector of Trilogi University. Currently, he served as Rector at University of Al Azhar Indonesia as well as President of Pusat Bahasa Mandiri University of Al Azhar Indonesia. In addition, he is also active in several national organizations, including Vice President of Dewan Pertimbangan Forum Rektor Indonesia, Vice President of ISSOSS (Islamic Country Society of Statistical Science) (2009-2014), and Chairman of the Advisory Committee of Yayasan Inovasi Teknologi (2007-present ). His research interest include: geoinformatics, spatial analysis, and statistical modelling. He has published any journal and conference papers and also coordinated some researches project in statistics.

I Wayan Mangku, IPB University

I WAYAN MANGKU is Professor of Departemen of Mathematics,  Faculty of Mathematics and Natural Sciences at Bogor Agricultural University. He completed his Master’s degree in Mathematical Modeling at School of Mathematics and Computer Science, Curtin University of Technology, Western Australia. He received his Ph.D degree in Mathematics at University of Amsterdam, The Netherlands. He is the head of Mathematical Modeling Division at Department of Mathematics, Bogor Agricultural University. His research interest include: stochastic process and mathematical statistics. He has published two books and more than 90 articles in scientific journals.

How to Cite
Ratnaningsih, D. J., Kurnia, A., Saefuddin, A., & Mangku, I. W. (2022). Mixed Models of Non-Proportional Hazard and Application in The Open Distance Education Students Retention Data. Journal of the Indonesian Mathematical Society, 28(3), 323–344. https://doi.org/10.22342/jims.28.3.1185.323-344
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