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

被引:0
|
作者
Cui, Yuzheng [1 ]
Lu, Jing [1 ]
Zhang, Jiwei [2 ]
Shi, Ningzhong [1 ]
Liu, Jia [1 ]
Meng, Xiangbin [1 ]
机构
[1] Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R China
[2] Northeast Normal Univ, Fac Educ, Changchun, Peoples R China
来源
FRONTIERS IN PSYCHOLOGY | 2022年 / 13卷
基金
中国国家自然科学基金;
关键词
item response theory; Ramsay curve; 3PNO model; marginal maximum likelihood estimation; stochastic approximation EM algorithm (SAEM); density estimation; ITEM RESPONSE THEORY; MAXIMUM-LIKELIHOOD-ESTIMATION; IRT; CONVERGENCE; PARAMETERS; FIT;
D O I
10.3389/fpsyg.2022.971126
中图分类号
B84 [心理学];
学科分类号
04 ; 0402 ;
摘要
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.
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页数:20
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