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Introduction: From Latent Classes to Cognitive Diagnostic Models

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Handbook of Diagnostic Classification Models

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

Abstract

This chapter provides historical and structural context for models and approaches presented in this volume, by presenting an overview of important predecessors of diagnostic classification models which we will refer to as DCM in this volume, or alternatively cognitive diagnostic models (CDMs). The chapter covers general notation and concepts central to latent class analysis, followed by an introduction of mastery models, ranging from deterministic to probabilistic forms. The ensuing sections cover knowledge state and rule space approaches, which can be viewed as deterministic skill-profile models. The chapter closes with a section on the multiple classification latent class model and the deterministic input noisy and (DINA) model.

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Notes

  1. 1.

    Class variables are represented as integers, but the use of integers do not imply any ordering here; only equivalence classes are used in the context of LCA.

References

  • Albert, D., & Lukas, J. (1999). Knowledge spaces: Theories, empirical research and applications. Mahwah, NJ: Erlbaum.

    Book  Google Scholar 

  • Allman, E. S., Matias, C., & Rhodes, J. A. (2009). Identifiability of parameters in latent structure models with many observed variables. The Annals of Statistics, 37(6A), 3099–3132. https://doi.org/10.1214/09-AOS689

    Article  Google Scholar 

  • Croon, M. A. (1990). Latent class analysis with ordered classes. British Journal of Mathematical and Statistical Psychology, 43, 171–192.

    Article  Google Scholar 

  • Dayton, C. M., & Macready, G. (2006). Latent class analysis in psychometrics. In C. R. Rao & S. Sinharay (Eds.), Handbook of statistics, Vol. 26: Psychometrics (pp. 45–79). Elsevier Science B.V.: Amsterdam, The Netherlands.

    Google Scholar 

  • de la Torre, J. (2009, March). DINA Model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34(1), 115–130.

    Article  Google Scholar 

  • Decarlo, L. T. (2011). On the analysis of fraction subtraction data: The DINA model, classification, latent class sizes, and the Q-matrix. Applied Psychological Measurement, 35, 8–26.

    Article  Google Scholar 

  • Doignon, J. P., & Falmagne, J. C. (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175–196.

    Article  Google Scholar 

  • Doignon, J. P., & Falmagne, J. C. (1998). Knowledge spaces. Berlin, Germany: Springer.

    Google Scholar 

  • Fang, G, Liu, J., & Ying, Z. (2017). On the identifiability of diagnostic classification models (Submitted on 5 Jun 2017) arXiv:1706.01240 [math.ST].

    Google Scholar 

  • Formann, A. K. (1985). Constrained latent class models: Theory and applications. British Journal of Mathematical and Statistical Psychology, 38, 87–111.

    Article  Google Scholar 

  • Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data. Journal of the American Statistical Association, 87(418), 476–486. https://doi.org/10.1080/01621459.1992.10475229

    Article  Google Scholar 

  • Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231.

    Article  Google Scholar 

  • Gutmann, M. U., & Hyvärinen, A. (2010). Noise-contrastive estimation: A new estimation principle for unnormalized statistical models. In International Conference on Artificial Intelligence and Statistics, 2010.

    Google Scholar 

  • Gutmann, M. U., & Hyvärinen, A. (2012). Noise-contrastive estimation of unnormalized statistical models, with applications to natural image statistics. Journal of Machine Learning Research, 13, 307–361.

    Google Scholar 

  • Haberman, S. J. (1979). Qualitative data analysis: Vol. 2. New developments. New York, NY: Academic.

    Google Scholar 

  • Haberman, S. J., von Davier, M., & Lee, Y. (2008). Comparison of multidimensional item response models: Multivariate normal ability distributions versus multivariate polytomous ability distributions. RR-08-45. ETS Research Report. https://doi.org/10.1002/j.2333-8504.2008.tb02131.x

  • 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 

  • Hagenaars, J. A. (1993). Loglinear models with latent variables. In Sage University Papers (Vol. 94). Newbury Park, CA: Sage Publications.

    Google Scholar 

  • Hagenaars, J. A., & McCutcheon, A. L. (Eds.). (2002). Applied latent class analysis models. Cambridge, UK: Cambridge University Press.

    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 

  • Langeheine, R., & Rost, J. (Eds.). (1988). Latent trait and latent class models. New York, NY: Plenum Press.

    Google Scholar 

  • Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston, MA: Houghton Mifflin Company.

    Google Scholar 

  • Leighton, J. P., Gierl, M. J., & Hunka, S. M. (2004). The attribute hierarchy model for cognitive assessment: A variation on Tatsuoka’s rule-space approach. Journal of Educational Measurement, 41, 205–237.

    Article  Google Scholar 

  • Macready, G. B., & Dayton, C. M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 2, 99–120.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Marsman, M., Borsboom, D., Kruis, J., Epskamp, S., van Bork, R., Waldorp, L. J., … Maris, G. (2018). An introduction to network psychometrics: Relating ising network models to item response theory models. Multivariate Behavioral Research, 53(1), 15–35. https://doi.org/10.1080/00273171.2017.1379379

    Article  Google Scholar 

  • Piaget, J. (1950). The psychology of intelligence (M. Piercy, Trans.). London, UK: Lowe & Brydone (Original work published 1947).

    Google Scholar 

  • Reis, S. M., McGuire, J. M., & Neu, T. W. (2000). Compensation strategies used by high ability students with learning disabilities. The Gifted Child Quarterly, 44, 123–134.

    Article  Google Scholar 

  • Rost, J., & Langeheine, R. (Eds.). (1997). Applications of latent trait and latent class models in the social sciences. Waxmann Publishers.

    Google Scholar 

  • Schrepp, M. (2005). About the connection between knowledge structures and latent class models. Methodology, 1, 92–102.

    Article  Google Scholar 

  • Tan, P.-N., Steinbach, M., & Kumar, V. (2005). Introduction to data mining. Boston, MA: Addison-Wesley.

    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 

  • Tatsuoka, K. K. (1985). A probabilistic model for diagnosing misconceptions by the pattern classification approach. Journal of Educational Statistics, 10(1), 55–73. https://doi.org/10.2307/1164930. https://www.jstor.org/stable/1164930

    Article  Google Scholar 

  • Tatsuoka, K. K. (1990). Toward an integration of item-response theory and cognitive error diagnosis. In N. Frederiksen, R. Glaser, A. Lesgold, & M. G. Shafto (Eds.), Diagnostic monitoring of skill and knowledge acquisition (pp. 453–488). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Tatsuoka, K. K. (2009). Cognitive assessment: An introduction to the rule space method. New York, NY: Routledge.

    Book  Google Scholar 

  • von Davier, M. (2009). Some notes on the reinvention of latent structure models as diagnostic classification models. Measurement, 7, 67–74.

    Google Scholar 

  • von Davier, M. (2013). The DINA model as a constrained general diagnostic model - two variants of a model equivalency. BJMSP, 67, 49–71. http://onlinelibrary.wiley.com/doi/10.1111/bmsp.12003/abstract

    Google Scholar 

  • von Davier, M. (2014). The log-linear cognitive diagnostic model (LCDM) as a special case of the general diagnostic model (GDM) (ETS research report series). http://onlinelibrary.wiley.com/doi/10.1002/ets2.12043/abstract

  • von Davier, M. (2018). Diagnosing diagnostic models: From von Neumann’s elephant to model equivalencies and network psychometrics. Measurement: Interdisciplinary Research and Perspectives, 16(1), 59–70. https://doi.org/10.1080/15366367.2018.1436827

    Article  Google Scholar 

  • von Davier, M., & Yamamoto, K. (2004). Partially observed mixtures of IRT models: An extension of the generalized partial credit model. Applied Psychological Measurement, 28(6), 389–406.

    Article  Google Scholar 

  • von Davier, M., & Carstensen, C. H. (2007). Multivariate and mixture distribution Rasch models–extensions and applications. (Editor of the volume). New York: Springer. ISBN: 978-0387-32916-1.

    Google Scholar 

  • von Davier, M., & Haberman, S. J. (2014). Hierarchical diagnostic classification models morphing into unidimensional ‘Diagnostic’ classification models – A commentary. Psychometrika, 79, 340. https://doi.org/10.1007/s11336-013-9363-z

    Article  Google Scholar 

  • von Davier, M., DiBello, L., & Yamamoto, K. (2008). Chapter 7: Reporting test outcomes using models for cognitive diagnosis. In J. Hartig, E. Klieme, & D. Leutner (Eds.) Assessment of competencies in educational contexts (pp. 151–176). Hogrefe & Huber Publishers.

    Google Scholar 

  • Wilson, M. (1989). Saltus: A psychometric model of discontinuity in cognitive development. Psychological Bulletin, 105, 276–289.

    Article  Google Scholar 

  • Xu, X., & von Davier, M. (2008). Comparing multiple-group multinomial loglinear models for multidimensional skill distributions in the general diagnostic model. RR-08-35, ETS Research Report.

    Google Scholar 

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Authors and Affiliations

  1. National Board of Medical Examiners (NBME), Philadelphia, PA, USA

    Matthias von Davier

  2. Teachers College, Columbia University, New York, NY, USA

    Young-Sun Lee

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  1. Matthias von Davier
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Correspondence to Matthias von Davier .

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Editors and Affiliations

  1. National Board of Medical Examiners (NBME), Philadelphia, PA, USA

    Matthias von Davier

  2. Teachers College, Columbia University, New York, NY, USA

    Young-Sun Lee

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von Davier, M., Lee, YS. (2019). Introduction: From Latent Classes to Cognitive Diagnostic Models. 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_1

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  • DOI: https://doi.org/10.1007/978-3-030-05584-4_1

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  • Online ISBN: 978-3-030-05584-4

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