Submitted Successfully!
To reward your contribution, here is a gift for you: A free trial for our video production service.
Thank you for your contribution! You can also upload a video entry or images related to this topic.
Version Summary Created by Modification Content Size Created at Operation
1 -- 46 2024-01-11 09:35:09 |
2 layout + 1027 word(s) 1073 2024-01-12 03:33:34 | |
3 Added description + 102 word(s) 1175 2024-01-12 04:40:54 | |
4 no change -102 word(s) 1073 2024-01-12 04:44:22 | |
5 layout Meta information modification 1073 2024-01-12 06:18:50 |

Video Upload Options

Do you have a full video?


Are you sure to Delete?
If you have any further questions, please contact Encyclopedia Editorial Office.
Chen, Y.; Liang, S. Cognitive Diagnosis Models. Encyclopedia. Available online: (accessed on 23 June 2024).
Chen Y, Liang S. Cognitive Diagnosis Models. Encyclopedia. Available at: Accessed June 23, 2024.
Chen, Yiming, Shuang Liang. "Cognitive Diagnosis Models" Encyclopedia, (accessed June 23, 2024).
Chen, Y., & Liang, S. (2024, January 11). Cognitive Diagnosis Models. In Encyclopedia.
Chen, Yiming and Shuang Liang. "Cognitive Diagnosis Models." Encyclopedia. Web. 11 January, 2024.
Cognitive Diagnosis Models

In the field of education, cognitive diagnosis is crucial for achieving personalized learning. The widely adopted DINA (Deterministic Inputs, Noisy And gate) model uncovers students’ mastery of essential skills necessary to answer questions correctly. However, existing DINA-based approaches overlook the dependency between knowledge points, and their model training process is computationally inefficient for large datasets.

cognitive diagnosis DINA model bayesian networks

1. Introduction

The emergence of the online education industry has revolutionized traditional educational approaches. Leveraging information technology, online education offers students convenient access to a vast array of courses and learning materials, thus promoting resource sharing and ensuring educational equity. However, with the exponential growth of available learning resources, accurately assessing a student’s mastery level of specific skills and knowledge has become a pressing challenge. Cognitive diagnosis models (CDMs), initially introduced by [1], have been developed to quantify the latent abilities that significantly impact students’ performance. CDMs [2][3] have gained widespread recognition and interest from both academic and industry domains by providing insights into the cognitive skills underlying students’ overall scores [4].
The DINA (Deterministic Inputs, Noisy And gate) model [5] is recognized as a prominent cognitive diagnosis approach, which effectively integrates the Q-matrix and students’ response patterns to assess their mastery level and identify potential error patterns within each knowledge point. By employing statistical techniques such as maximum likelihood estimation [6], the DINA model equips educators with a comprehensive cognitive diagnostic tool, enabling the formulation of personalized teaching strategies that cater to individuals’ performance across diverse knowledge points.

2. Different Models of Cognitive Diagnosis

Cognitive diagnosis, initially proposed by educational psychologists for psychological measurement, has its roots in the 1990s. Frederiksen et al. [7] were credited with formally introducing the theories and concepts related to cognitive diagnosis in 1993, while Nichols et al. [8] further provided a comprehensive summary and categorization of these theories and concepts in 1995. Leighton et al. [9] considered CDM as a promising evaluation model that can delve into the underlying structure of a field and identify problems and areas that need improvement in 2007. Lee et al. [10] proposed that tests informed by the Cognitive Diagnosis Algorithm (CDA) can specify the underlying knowledge structure behind the overall test score, and this specification can serve as feedback to meet individual and group needs through remedial instruction and improve instruction to enhance learning and competency in 2009. As a diagnostic approach to assessment, CDA needs statistical and mathematical models to operationalize the assumptions. CDMs are psychometric models that make use of an item response pattern in order to determine test-takers’ cognitive abilities [11]. In all CDA studies, the selection of statistical models is a critical step and requires close attention and consideration of model selection criteria. However, in most CDA studies, tests applying a predetermined CDM are chosen based on the characteristics of the model and the practicality issue. So Li et al. [12] carefully studied the considerations required for CDM selection for reading comprehension tests and found that when the relationship between cognitive skills is not completely clear, it is safe to use a saturated (more complex) CDM, which can flexibly adapt to different types of relationships between skills in 2016. Currently, cognitive diagnosis can be defined in both broad and narrow terms. Broadly speaking, cognitive diagnosis leverages modern technologies such as computer-based testing and statistical methods to assess users’ cognitive abilities and structures [13][14]. On the other hand, in a narrower sense, cognitive diagnosis classifies users based on their mastery level of specific knowledge points, with the classification results used for personalized educational interventions.
The application of cognitive diagnosis in the education industry has led to a shift towards personalized education in traditional online classrooms [15][16]. Cognitive diagnosis models can be differentiated from two perspectives. Firstly, they can be classified as continuous diagnosis models or discrete diagnosis models, depending on their ability to diagnose continuous scores. Secondly, cognitive diagnosis models can be classified based on their approach to handling dimensions of students’ cognitive abilities. This categorization results in one-dimensional skill diagnosis models and multidimensional skill diagnosis models. Currently, there are more than 60 cognitive diagnosis models available. These models include the rule-based model, attribute hierarchy model, Deterministic Inputs, Noisy And gate (DINA) model, as well as various variations [17][18] such as the Fuzzy CDF model [19]. Improved versions of the DINA model, such as the HO-DINA [20], P-DINA [21], G-DINA [22], and Incremental DINA (I-DINA) model [23], are also among the existing models used in cognitive diagnosis research.
The history of Bayesian networks dates back to the early 1980s. In 1988, Pearl et al. [24] first introduced the fundamental concepts and inference methods of Bayesian networks in their seminal paper. Notably, Pearl’s work also introduced the concept of the “causal graph”, which expanded probabilistic graph models to incorporate causal relationships, thereby establishing the groundwork for further development. In the 1990s, research in the field expanded from representation issues to encompass inference and learning [25], making Bayesian networks more practical in various applications. With the advancement of computational power and the exponential growth of data in the 21st century, Bayesian networks have found widespread application in diverse domains such as medicine [26], finance [27], and natural language processing [28]. Research in the field has also made significant progress in reasoning, learning, and the application of Bayesian networks [29].
In recent research, the integration of Bayesian networks and the DINA model has gained attention, with notable applications in student modeling, knowledge tracing, and skill topology. For instance, Conati et al. [30] applied Bayesian networks to the Andes project [31], an intelligent educational system focused on Newtonian physics, to model uncertainty within students’ reasoning and learning processes. In the domain of knowledge tracing [32], Pelánek [33] introduced Bayesian Knowledge Tracing (BKT), which employed Bayesian networks to infer latent student variables within knowledge-tracing models. Furthermore, Käser et al. [32] utilized dynamic Bayesian networks (DBN) to model skill topology in knowledge tracking. While these works have made significant contributions to the application of Bayesian networks, their main focus lies in student modeling, knowledge tracing, and skill topology. In parallel, recent breakthroughs in asynchronous federated meta-learning, exemplified by AFMeta, have effectively addressed issues such as straggler and over-fitting, resulting in a substantial improvement in model performance and a notable reduction in learning time [34]. In the field of education-based information analysis, the examination of student learning assessment methods based on text data has emerged as a crucial research area. Liu et al. [35] introduced an innovative learning evaluation method based on real-time text data attributes, overcoming the limitations of traditional evaluation methods. The outcomes highlight the superior effectiveness of utilizing real-time attribute text data in measuring students’ learning outcomes.


  1. Templin, J.L.; Henson, R.A. Measurement of psychological disorders using cognitive diagnosis models. Psychol. Methods 2006, 11, 287.
  2. Wang, F.; Huang, Z.; Liu, Q.; Chen, E.; Yin, Y.; Ma, J.; Wang, S. Dynamic Cognitive Diagnosis: An Educational Priors-Enhanced Deep Knowledge Tracing Perspective. IEEE Trans. Learn. Technol. 2023, 16, 306–323.
  3. Liu, Y.; Zhang, T.; Wang, X.; Yu, G.; Li, T. New development of cognitive diagnosis models. Front. Comput. Sci. 2023, 17, 171604.
  4. Luo, J.; Hubaux, J.P. A survey of research in inter-vehicle communications. In Embedded Security in Cars: Securing Current and Future Automotive IT Applications; Springer: Berlin/Heidelberg, Germany, 2006; pp. 111–122.
  5. De La Torre, J. DINA model and parameter estimation: A didactic. J. Educ. Behav. Stat. 2009, 34, 115–130.
  6. Wafa, M.N.; Zia, Z.; Frozan, F. Consistency and Ability of Students Using DINA and DINO Models. Eur. J. Math. Stat. 2023, 4, 7–13.
  7. Frederiksen, N.; Mislevy, R.J.; Bejar, I.I. Test Theory for a New Generation of Tests; Routledge: London, UK, 2012.
  8. Nichols, P.D.; Chipman, S.F.; Brennan, R.L. Cognitively Diagnostic Assessment; Routledge: London, UK, 2012.
  9. Leighton, J.; Gierl, M. Cognitive Diagnostic Assessment for Education: Theory and Applications; Cambridge University Press: Cambridge, UK, 2007.
  10. Lee, Y.W.; Sawaki, Y. Cognitive diagnosis approaches to language assessment: An overview. Lang. Assess. Q. 2009, 6, 172–189.
  11. Gu, Z. Maximizing the Potential of Multiple-Choice Items for Cognitive Diagnostic Assessment; University of Toronto Canada: Toronto, ON, Canada, 2011.
  12. Li, H.; Hunter, C.V.; Lei, P.W. The selection of cognitive diagnostic models for a reading comprehension test. Lang. Test. 2016, 33, 391–409.
  13. Yang, Y. Modeling Nonignorable Missingness with Response Times Using Tree-Based Framework in Cognitive Diagnostic Models; Columbia University: New York, NY, USA, 2023.
  14. Yang, S.; Wei, H.; Ma, H.; Tian, Y.; Zhang, X.; Cao, Y.; Jin, Y. Cognitive diagnosis-based personalized exercise group assembly via a multi-objective evolutionary algorithm. IEEE Trans. Emerg. Top. Comput. Intell. 2023, 7, 829–844.
  15. Qi, T.; Ren, M.; Guo, L.; Li, X.; Li, J.; Zhang, L. ICD: A new interpretable cognitive diagnosis model for intelligent tutor systems. Expert Syst. Appl. 2023, 215, 119309.
  16. Ma, H.; Huang, Z.; Tang, W.; Zhu, H.; Zhang, H.; Li, J. Predicting Student Performance in Future Exams via Neutrosophic Cognitive Diagnosis in Personalized E-learning Environment. IEEE Trans. Learn. Technol. 2023, 16, 680–693.
  17. Gao, W.; Wang, H.; Liu, Q.; Wang, F.; Lin, X.; Yue, L.; Zhang, Z.; Lv, R.; Wang, S. Leveraging Transferable Knowledge Concept Graph Embedding for Cold-Start Cognitive Diagnosis. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, Taipei, Taiwan, 23–27 July 2023; pp. 983–992.
  18. Wang, S.; Zeng, Z.; Yang, X.; Zhang, X. Self-supervised graph learning for long-tailed cognitive diagnosis. In Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA, 7–14 February 2023; Volume 37, pp. 110–118.
  19. Wu, R.; Liu, Q.; Liu, Y.; Chen, E.; Su, Y.; Chen, Z.; Hu, G. Cognitive modelling for predicting examinee performance. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, Buenos Aires, Argentina, 25–31 July 2015.
  20. De La Torre, J.; Douglas, J.A. Higher-order latent trait models for cognitive diagnosis. Psychometrika 2004, 69, 333–353.
  21. Tu, D.B.; Cai, Y.; Dai Hai-Qi, D. A polytomous cognitive diagnosis model: P-DINA model. Acta Psychol. Sin. 2010, 42, 1011.
  22. Aryadoust, V. A cognitive diagnostic assessment study of the listening test of the Singapore–Cambridge general certificate of education O-level: Application of DINA, DINO, G-DINA, HO-DINA, and RRUM. Int. J. List. 2021, 35, 29–52.
  23. Wang, C.; Liu, Q.; Chen, E.H.; Huang, Z.Y.; Zhu, T.Y.; Su, Y.; Hu, G.P. The rapid calculation method of DINA model for large scale cognitive diagnosis. Acta Electonica Sin. 2018, 46, 1047.
  24. Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference; Morgan Kaufmann: Burlington, MA, USA, 1988.
  25. Murphy, K.P. Inference and Learning in Hybrid Bayesian Networks; Citeseer: Berkeley, CA, USA, 1998.
  26. Tang, J.; Liu, X.; Wang, W. COVID-19 medical waste transportation risk evaluation integrating type-2 fuzzy total interpretive structural modeling and Bayesian network. Expert Syst. Appl. 2023, 213, 118885.
  27. Chan, L.S.; Chu, A.M.; So, M.K. A moving-window bayesian network model for assessing systemic risk in financial markets. PLoS ONE 2023, 18, e0279888.
  28. Kamil, M.Z.; Taleb-Berrouane, M.; Khan, F.; Amyotte, P.; Ahmed, S. Textual data transformations using natural language processing for risk assessment. Risk Anal. 2023, 43, 2033–2052.
  29. Yang, H.; Qi, T.; Li, J.; Guo, L.; Ren, M.; Zhang, L.; Wang, X. A novel quantitative relationship neural network for explainable cognitive diagnosis model. Knowl. Based Syst. 2022, 250, 109156.
  30. Conati, C.; Gertner, A.; Vanlehn, K. Using Bayesian networks to manage uncertainty in student modeling. User Model. User Adapt. Interact. 2002, 12, 371–417.
  31. VanLehn, K.; Lynch, C.; Schulze, K.; Shapiro, J.A.; Shelby, R.; Taylor, L.; Treacy, D.; Weinstein, A.; Wintersgill, M. The Andes physics tutoring system: Lessons learned. Int. J. Artif. Intell. Educ. 2005, 15, 147–204.
  32. Käser, T.; Klingler, S.; Schwing, A.G.; Gross, M. Beyond knowledge tracing: Modeling skill topologies with bayesian networks. In Proceedings of the Intelligent Tutoring Systems: 12th International Conference, ITS 2014, Honolulu, HI, USA, 5–9 June 2014; Springer: Berlin/Heidelberg, Germany, 2014; pp. 188–198.
  33. Pelánek, R. Bayesian knowledge tracing, logistic models, and beyond: An overview of learner modeling techniques. User Model. User Adapt. Interact. 2017, 27, 313–350.
  34. Liu, S.; Qu, H.; Chen, Q.; Jian, W.; Liu, R.; You, L. AFMeta: Asynchronous Federated Meta-learning with Temporally Weighted Aggregation. In Proceedings of the 2022 IEEE Smartworld, Ubiquitous Intelligence & Computing, Scalable Computing & Communications, Digital Twin, Privacy Computing, Metaverse, Autonomous & Trusted Vehicles (SmartWorld/UIC/ScalCom/DigitalTwin/PriComp/Meta), Haikou, China, 15–18 December 2022; IEEE: Piscataway, NJ, USA, 2022; pp. 641–648.
  35. Liu, S.; He, T.; Li, J.; Li, Y.; Kumar, A. An effective learning evaluation method based on text data with real-time attribution-a case study for mathematical class with students of junior middle school in China. ACM Trans. Asian Low Resour. Lang. Inf. Process. 2023, 22, 1–22.
Contributors MDPI registered users' name will be linked to their SciProfiles pages. To register with us, please refer to : ,
View Times: 203
Revisions: 5 times (View History)
Update Date: 12 Jan 2024
Video Production Service