Title: A Metropolis within Gibbs algorithm for knowledge discovery in language assessments

Authors: Mengta Chung

Addresses: Department of Artificial Intelligence, CTBC Business School, 600 Sec. 3 Taijiang Blvd., Annan District, Tainan, Taiwan

Abstract: The reduced reparameterised unified model (RRUM) has been frequently used in language assessment studies. The objective of this research is to advance an MCMC algorithm for the Bayesian RRUM. The algorithm starts with estimating correlated attributes. Using a saturated model and a binary decimal conversion, the algorithm transforms possible attribute patterns to a multinomial distribution. Along with the likelihood of an attribute pattern, a Dirichlet distribution is used as the prior to sample from the posterior. The Dirichlet distribution is constructed using Gamma distributions. Correlated attributes of examinees are generated using the inverse transform sampling. Model parameters are estimated using the Metropolis within Gibbs sampler sequentially. Two simulation studies are conducted to evaluate the performance of the algorithm. The simulation studies show that as sample size increases, the measure of accuracy increases. The algorithm developed in this research is implemented in R.

Keywords: cognitive diagnosis model; CDM; reparameterised unified model; RUM; reduced version of the RUM; RRUM; Q-matrix; Bayesian; MCMC.

DOI: 10.1504/IJMMNO.2020.10031724

International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.4, pp.331 - 341

Received: 08 Feb 2019
Accepted: 29 Sep 2019

Published online: 28 Oct 2020 *

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