Approximate Bayesian Inference for Educational Attainment Models

Abstract

- The rapidly expanding volume of educational testing data from online assessments has posed a problem for researchers in modern education. Their main goal is to utilise this information in a timely and adaptive manner to infer skills mastery, improving learning facilities and adapting them to individual learners. Over the past few years, a number of static statistical models have been proposed for extracting knowledge about skills mastery from item response data. However, realistic models typically lead to complex, computationally expensive fitting methods such as MCMC. So these methods will not tend to scale well for streaming data and large-scale real-time systems. The main objective of this paper is to develop approximate Bayesian inference based on the Laplace approximation method (LA), which allows faster inference. The LA estimation method's performance for the one-parameter logistic item response theory (IRT) model has been compared with the MCMC method in a simulation study. Based on the results of several comparison criterion methods such as bias, RMSE and Kendell's measurement distance, the performance of the LA is very good in small, moderate, and relatively large sample size settings. The LA approximately estimated abilities results are very close to the actual values and sometimes even better than the estimated abilities resulting from MCMC. In addition, LA resulted in between a 120 to 900 times speedup over MCMC, making it a more practical alternative for large educational testing datasets. test