MOOC学习者辍学模式的建模
Modelling the Dropout Patterns of MOOC Learners
摘要：
我们采用生存分析的观看持续时间的大规模开放的在线课程。经验久期数据的风险函数受浴盆曲线支配，其尾部存在林迪效应。为了理解这些特征背后的进化机制，我们将学习者分为两类，由于他们的不同分布的观看时间，即对数正态分布和幂律指数截止。给出了两个随机微分方程，分别描述了两类人的观看时长增长规律。学习者的期望时长变化率服从对数正态分布，与其过去的时长有关，其余学习者的期望时长变化率与时间成反比。方程的解预测观看持续时间分布的特征，以及风险函数的特征。该方程还分别揭示了两类人观看行为的记忆性和无记忆性。
英文摘要：
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.
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