Modelling the Dropout Patterns of MOOC Learners

TL;DR

This paper uses survival analysis to model MOOC learners' viewing durations, revealing distinct patterns and underlying mechanisms, including the Lindy effect and memory properties, through differential equations.

Contribution

It introduces a novel differential equation framework to describe and predict MOOC learners' viewing duration distributions based on their behavioral classes.

Findings

Hazard function exhibits a bathtub shape and Lindy effect.

Learners' viewing durations follow lognormal or power law with exponential cutoff distributions.

The models reveal memory and memoryless behaviors in learner groups.

Abstract

We adopted survival analysis for the viewing durations of massive open online courses. The hazard function of empirical duration data is dominated by a bathtub curve and has the Lindy effect in its tail. To understand the evolutionary mechanisms underlying these features, we categorized learners into two classes due to their different distributions of viewing durations, namely lognormal distribution and power law with exponential cutoff. Two random differential equations are provided to describe the growth patterns of viewing durations for the two classes respectively. The expected duration change rate of the learners featured by lognormal distribution is supposed to be dependent on their past duration, and that of the rest learners is supposed to be inversely proportional to time. Solutions to the equations predict the features of viewing duration distributions, and those of the hazard function. The equations also reveal the feature of memory and that of memorylessness for the viewing behaviors of the two classes respectively.