The Q-Matrix Anchored Mixture Rasch Model

Frontiers in Psychology

Ming-Chi Tseng¹  Wen-Chung Wang² 

[1] National University of Tainan, Tainan, Taiwan;The Education University of Hong Kong, Tai Po, Hong Kong;

关键词: Q-matrix anchored mixture Rasch model;    Q-matrix;    anchor;    mixture Rasch model;    Rasch model;   

DOI  :  10.3389/fpsyg.2021.564976

来源: Frontiers

【 摘 要 】

Mixture item response theory (IRT) models include a mixture of latent subpopulations such that there are qualitative differences between subgroups but within each subpopulation the measure model based on a continuous latent variable holds. Under this modeling framework, students can be characterized by both their location on a continuous latent variable and by their latent class membership according to Students’ responses. It is important to identify anchor items for constructing a common scale between latent classes beforehand under the mixture IRT framework. Then, all model parameters across latent classes can be estimated on the common scale. In the study, we proposed Q-matrix anchored mixture Rasch model (QAMRM), including a Q-matrix and the traditional mixture Rasch model. The Q-matrix in QAMRM can use class invariant items to place all model parameter estimates from different latent classes on a common scale regardless of the ability distribution. A simulation study was conducted, and it was found that the estimated parameters of the QAMRM recovered fairly well. A real dataset from the Certificate of Proficiency in English was analyzed with the QAMRM, LCDM. It was found the QAMRM outperformed the LCDM in terms of model fit indices.

【 授权许可】

CC BY