The Q-matrix anchored mixture rasch model

Ming-Chi TSENG, Wen Chung WANG

Research output: Contribution to journalArticlespeer-review

2 Citations (Scopus)


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. Copyright © 2021 Tseng and Wang.
Original languageEnglish
Article number564976
JournalFrontiers in Psychology
Early online date04 Mar 2021
Publication statusPublished - Mar 2021


Tseng, M.-C., & Wang, W.-C. (2021). The Q-matrix anchored mixture Rasch model. Frontiers in Psychology, 12. Retrieved from


  • Q-matrix anchored mixture Rasch model
  • Q-matrix
  • Anchor
  • Mixture Rasch model
  • Rasch model


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