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A Multiple Hurdle Model for Students’ Conversions in Online English Learning Materials
The present study provides a multiple hurdle model which computationally explains complex patterns of students’ engagement levels in online learning materials. It has been empirically known that online learning log data such as login counts and the number of learning contents studied by students quite often deviate from ordinary discrete probabilistic distributions such as a Poisson distribution and a negative binomial distribution. As an underlying mechanism of this empirical fact, the present study posits that there are latent sub-processes to obtain learning outcomes, which we call micro conversions, and between them, the model also assumes hurdles that students clear and fail. This modeling framework was statistically implemented as a finite mixture distribution model that mixes a hurdle negative binomial distribution and an ordinary negative binomial distribution. Using Bayesian modeling with the Hamiltonian Monte Carlo method, the model was fitted to the real login data of 899 students in Hiroshima university and achieved a relatively good fit.
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