Statistics and Its Interface

Volume 13 (2020)

Number 1

Bayesian longitudinal multilevel item response modeling approach for studying individual growth differences

Pages: 1 – 16



Shuang Qu (School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China; and School of Mathematics, Changchun Normal University, Changchun, Jilin, China)

Jiwei Zhang (School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan, China)

Jian Tao (School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China)


A longitudinal multilevel item response model is proposed for measuring changes in individual growth over time. To estimate the model parameters, a combined Bayesian procedure is developed. The deviance information criterion (DIC) and the widely applicable information criterion (WAIC) are used to assess the competing models. The simulation results show that the combined Bayesian estimation method performs perfectly in terms of recovering model parameters under various design conditions. Finally, a longitudinal dataset about the development of achievement in mathematics illustrates the significance and implementation of the proposed procedure.


Item response theory, Longitudinal multilevel model, Markov chain Monte Carlo, Metropolis-Hastings within Gibbs algorithm

This work was supported by the National Natural Science Foundation of China (grant number 11571069) and Natural Science Foundation of Changchun Normal University.

Received 11 July 2018

Accepted 14 June 2019

Published 7 November 2019