A stochastic approximation expectation maximization algorithm for estimating Ramsay-curve three-parameter normal ogive model with non-normal latent trait distributions
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作者:
Cui, Yuzheng
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Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R ChinaNortheast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R China
Cui, Yuzheng
[1
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Lu, Jing
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Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R ChinaNortheast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R China
Lu, Jing
[1
]
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Zhang, Jiwei
[2
]
Shi, Ningzhong
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Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R ChinaNortheast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R China
Shi, Ningzhong
[1
]
Liu, Jia
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Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R ChinaNortheast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R China
Liu, Jia
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Meng, Xiangbin
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Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R ChinaNortheast Normal Univ, Sch Math & Stat, Key Lab Appl Stat, Minist Educ, Changchun, Peoples R China
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
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.