AUTHOR=Cui Yuzheng , Lu Jing , Zhang Jiwei , Shi Ningzhong , Liu Jia , Meng Xiangbin TITLE=A stochastic approximation expectation maximization algorithm for estimating Ramsay-curve three-parameter normal ogive model with non-normal latent trait distributions JOURNAL=Frontiers in Psychology VOLUME=13 YEAR=2022 URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.971126 DOI=10.3389/fpsyg.2022.971126 ISSN=1664-1078 ABSTRACT=

In the estimation of item response models, the normality of latent traits is frequently assumed. However, this assumption may be untenable in real testing. In contrast to the conventional three-parameter normal ogive (3PNO) model, a 3PNO model incorporating Ramsay-curve item response theory (RC-IRT), denoted as the RC-3PNO model, allows for flexible latent trait distributions. We propose a stochastic approximation expectation maximization (SAEM) algorithm to estimate the RC-3PNO model with non-normal latent trait distributions. The simulation studies of this work reveal that the SAEM algorithm produces more accurate item parameters for the RC-3PNO model than those of the 3PNO model, especially when the latent density is not normal, such as in the cases of a skewed or bimodal distribution. Three model selection criteria are used to select the optimal number of knots and the degree of the B-spline functions in the RC-3PNO model. A real data set from the PISA 2018 test is used to demonstrate the application of the proposed algorithm.