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The G-DINA Model Framework

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Part of the book series: Methodology of Educational Measurement and Assessment ((MEMA))

Abstract

The development of cognitive diagnosis models (CDMs) has been prolific since the turn of the century; however, they have often been developed in such a way that they lack an overall connective framework. The purpose of this chapter is to review the G-DINA framework. As a general model, it subsumes several simpler and widely-known CDMs; as a general framework, it has also served as the foundation for a variety of model extensions and new methodological developments. We will also discuss associated topics, which include model estimation, Q-matrix validation, computerized adaptive testing, and model selection as they relate to the reviewed models.

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References

  • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory (pp. 267–281). Budapest, Hungary: Akademiai Kiado.

    Google Scholar 

  • Beck, L. W. (1943). The principle of parsimony in empirical science. The Journal of Philosophy, 40, 617–633.

    Article  Google Scholar 

  • Ben-Simon, A., Budescu, D. V., & Nevo, B. A. (1997). Comparative study of measures of partial knowledge in multiple choice tests. Applied Psychological Measurement, 21, 65–88.

    Article  Google Scholar 

  • Chen, J., & de la Torre, J. (2013). A general cognitive diagnosis model for expert-defined polytomous attributes. Applied Psychological Measurement, 37, 419–437.

    Article  Google Scholar 

  • Chen, J., de la Torre, J., & Zhang, Z. (2013). Relative and absolute fit evaluation in cognitive diagnosis modeling. Journal of Educational Measurement, 50, 123–140.

    Article  Google Scholar 

  • Cheng, Y. (2009). When cognitive diagnosis meets computerized adaptive testing: CD-CAT. Psychometrika, 74, 619–632.

    Article  Google Scholar 

  • de la Torre, J. (2008). An empirically based method of Q-matrix validation for the DINA model: Development and applications. Journal of Educational Measurement, 45, 343–362.

    Article  Google Scholar 

  • de la Torre, J. (2009). DINA model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34, 115–130.

    Article  Google Scholar 

  • de la Torre, J. (2010, July). The partial-credit DINA model. Paper Presented at the International Meeting of the Psychometric Society, Athens, GA.

    Google Scholar 

  • de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179–199.

    Article  Google Scholar 

  • de la Torre, J. (2015, December). Cognitively diagnostic assessment and cognitive diagnosis modeling: An example from start to finish. Invited Presentation at the Global Chinese Conference on Educational Information and Assessment and Chinese Association of Psychological Testing Annual Conference, Taichung, Taiwan.

    Google Scholar 

  • de la Torre, J., & Chiu, C.-Y. (2016). A general method of empirical Q-matrix validation. Psychometrika, 81, 253–273.

    Article  Google Scholar 

  • de la Torre, J., & Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333–353.

    Article  Google Scholar 

  • de la Torre, J., & Douglas, J. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595–624.

    Article  Google Scholar 

  • de la Torre, J., & Lee, Y.-S. (2013). Evaluating the Wald test for item-level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50, 355–373.

    Article  Google Scholar 

  • de la Torre, J., & Ma, W. (2016, August). Cognitive diagnosis modeling: A general framework approach and its implementation in R. A Short Course at the Fourth Conference on Statistical Methods in Psychometrics, Columbia University, New York.

    Google Scholar 

  • de la Torre, J., & Ma, W. (2017, November). Do I complete Q ? Invited Presentation at the Fifth Conference on the Statistical Methods in Psychometrics, Department of Statistics, Columbia University, New York.

    Google Scholar 

  • de la Torre, J., & Minchen, N. D. (2014). Cognitively diagnostic assessments and the cognitive diagnosis model framework. Psicología Educativa, 20, 89–97.

    Article  Google Scholar 

  • de la Torre, J., & Minchen, N. D. (2016, May). Modeling response time in cognitive diagnosis. Invited Presentation at the Graduate Institute of Educational Measurement and Statistics Colloquium, National Taichung University of Education, Taiwan.

    Google Scholar 

  • Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301–321.

    Article  Google Scholar 

  • Hansen, M. (2013). Hierarchical item response models for cognitive diagnosis. (Unpublished doctoral dissertation). Los Angeles: University of California.

    Google Scholar 

  • Hartz, S. M. (2002). A Bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality (Unpublished doctoral dissertation).

    Google Scholar 

  • Henson, R., Templin, J., & Willse, J. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74, 191–210.

    Article  Google Scholar 

  • Hou, L., & Terzi, R. (2017, April). Examining DIF in the proportional reasoning test using various Wald test formulations. Paper Presented at the Meeting of National Council on Measurement in Education, San Antonio, TX.

    Google Scholar 

  • Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258–272.

    Article  Google Scholar 

  • Kaplan, M., de la Torre, J., & Barrada, J. R. (2015). New item selection methods for cognitive diagnosis computerized adaptive testing. Applied Psychological Measurement, 39(3), 167–188.

    Article  Google Scholar 

  • Ma, W. (2018). A diagnostic tree model for polytomous responses with multiple strategies. British Journal of Mathematical and Statistical Psychology. Advanced online publication. https://doi.org/10.1111/bmsp.12137

  • Ma, W., & de la Torre, J. (2016). A sequential cognitive diagnosis model for polytomous responses. British Journal of Mathematical and Statistical Psychology, 69, 253–275.

    Article  Google Scholar 

  • Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection, and attribute classification. Applied Psychological Measurement, 40, 200–217.

    Article  Google Scholar 

  • Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187–212.

    Article  Google Scholar 

  • Minchen, N. D., & de la Torre, J. (2018). A general cognitive diagnosis model for continuous-response data. Measurement: Interdisciplinary research and perspective, 16, 30–44.

    Google Scholar 

  • Minchen, N. D., de la Torre, J., & Liu, Y. (2017). A cognitive diagnosis model for continuous response. Journal of Educational and Behavioral Statistics, 42, 651–677.

    Article  Google Scholar 

  • Noel, Y. (2014). A beta unfolding model for continuous bounded responses. Psychometrika, 79, 647–674.

    Article  Google Scholar 

  • Noel, Y., & Dauvier, B. (2007). A beta item response model for continuous bounded responses. Applied Psychological Measurement, 31, 47–73.

    Article  Google Scholar 

  • Samejima, F. (1973). Homogeneous case of the continuous response model. Psychometrika, 38, 203–219.

    Article  Google Scholar 

  • Tatsuoka, K. K. (1983). Rule-space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20, 345–354.

    Article  Google Scholar 

  • Templin, J. L., & Henson, R. A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287–305.

    Article  Google Scholar 

  • Templin, J. L., Rupp, A., Henson, R., Jang, E., & Ahmed, M. (2008, March). Cognitive diagnosis models for nominal response data. Paper Presented at the Annual Meeting of the National Council on Measurement in Education, New York.

    Google Scholar 

  • Tjoe, H., & de la Torre, J. (2013a). Designing cognitively-based proportional reasoning problems as an application of modern psychological measurement models. Journal of Mathematics Education, 6, 17–22.

    Google Scholar 

  • Tjoe, H., & de la Torre, J. (2013b). The identification and validation process of proportional reasoning attributes: An application of a cognitive diagnosis modeling framework. Mathematics Education Research Journal, 26, 237–255.

    Article  Google Scholar 

  • von Davier, M. (2008). A general diagnostic model applied to language testing data. British Journal of Mathematical and Statistical Psychology, 61, 287–307.

    Article  Google Scholar 

  • von Davier, M. (2014). The log-linear cognitive diagnostic model (LCDM) as a special case of the general diagnostic model (GDM) (Research Report No. RR-14-40). Princeton, NJ: Educational Testing Service. Retrieved from https://doi.org/10.1002/ets2.12043

    Google Scholar 

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Correspondence to Jimmy de la Torre .

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Torre, J.d., Minchen, N.D. (2019). The G-DINA Model Framework. In: von Davier, M., Lee, YS. (eds) Handbook of Diagnostic Classification Models. Methodology of Educational Measurement and Assessment. Springer, Cham. https://doi.org/10.1007/978-3-030-05584-4_7

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  • DOI: https://doi.org/10.1007/978-3-030-05584-4_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05583-7

  • Online ISBN: 978-3-030-05584-4

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