A stochastic approximation expectation maximization algorithm for estimating Ramsay-curve three-parameter normal ogive model with non-normal latent trait distributions

Yuzheng Cui; Jing Lu; Jiwei Zhang; Ningzhong Shi; Jia Liu; Xiangbin Meng

doi:10.3389/fpsyg.2022.971126

A stochastic approximation expectation maximization algorithm for estimating Ramsay-curve three-parameter normal ogive model with non-normal latent trait distributions

Front Psychol. 2022 Nov 24:13:971126. doi: 10.3389/fpsyg.2022.971126. eCollection 2022.

Authors

Yuzheng Cui¹, Jing Lu¹, Jiwei Zhang², Ningzhong Shi¹, Jia Liu¹, Xiangbin Meng¹

Affiliations

¹ Key Laboratory of Applied Statistics of Ministry of Education, School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
² Faculty of Education, Northeast Normal University, Changchun, China.

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.

Keywords: 3PNO model; Ramsay curve; density estimation; item response theory; marginal maximum likelihood estimation; stochastic approximation EM algorithm (SAEM).