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Explanatory Cognitive Diagnostic Models

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

Abstract

Student- and school-level information from large-scale educational data have been shown to explain trends in test taker performance and to inform factors that can enhance the learning environment. This study presents methods to specify and model predictive relationships of latent and observed explanatory variables within a cognitive diagnostic model, referred to as the Explanatory Cognitive Diagnostic Model (ECDM) framework. Explanatory factors can be incorporated simultaneously as observed covariates or latent variables (estimated using item response theory) that can explain patterns of attribute mastery. This chapter is divided into two studies that demonstrate real-world application using large-scale international testing data and simulation studies, which examine parameter recovery and classification for varying sample sizes and number of attributes. Simultaneous estimation of multiple observed and latent (using dichotomous and polytomous items as indicators for the latent construct) predictors show consistency in attribute classification and parameter recovery. Extensions of the ECDM framework are discussed.

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Notes

  1. 1.

    Available at https://timssandpirls.bc.edu/TIMSS2007/idb_ug.html

References

  • Bedeian, A. G., Day, D. V., & Kelloway, E. K. (1997). Correcting for measurement error attenuation in structural equation models: Some important reminders. Educational and Psychological Measurement, 57, 785–799.

    Article  Google Scholar 

  • Chang, M., & Kim, S. (2009). Computer access and computer use for science performance of racial and linguistic minority students. Journal of Educational Computing Research, 40, 469–501.

    Article  Google Scholar 

  • Clogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 311–359). New York, NY: Plenum Press.

    Chapter  Google Scholar 

  • Dayton, C. M., & MacReady, G. B. (1988). A latent class covariate model with applications to criterion-referenced testing. In R. Langeheine & J. Rost (Eds.), Latent trait and latent class models (pp. 129–143). New York, NY: Plenum Publications Inc.

    Chapter  Google Scholar 

  • De Boeck, P., & Wilson, M. (2004). Explanatory item response models: A generalized linear and nonlinear approach. New York, NY: Springer.

    Book  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. (2011). The generalized DINA model framework. Psychometrika, 76, 179–199.

    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 

  • 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 

  • DiBello, L. V., Roussos, L. A., & Stout, W. (2007). Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao & S. Sinharay (Eds.), Handbook of statistics: Vol. 26. Psychometrics (pp. 979–1030). Amsterdam, The Netherlands: Elsevier.

    Google Scholar 

  • Fox, J.-P., & Glas, C. A. W. (2003). Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika, 68(2), 169–191.

    Article  Google Scholar 

  • Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 333–352.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Huang, G. H., & Bandeen-Roche, K. (2004). Building an identifiable latent class model with covariate effects on underlying and measured variables. Psychometrika, 69, 5–32.

    Article  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 

  • Mislevy, R. J., Johnson, E. G., & Muraki, E. (1992). Scaling procedures in NAEP. Journal of Educational and Behavioral Statistics, 17(2), 131–154.

    Google Scholar 

  • Park, H., Lawson, D., & Williams, H. E. (2012). Relationship between technology, parent, education, self-confidence, and academic aspiration of Hispanic immigrant students. Journal of Educational Computing Research, 46(3), 255–265.

    Article  Google Scholar 

  • Park, Y. S., & Lee, Y.-S. (2014). An extension of the DINA model using covariates: Examining factors affecting response probability and latent classification. Applied Psychological Measurement, 38, 376–390.

    Article  Google Scholar 

  • Park, Y. S., Xing, K., & Lee, Y.-S. (2018). Explanatory cognitive diagnostic models: Incorporating latent and observed predictors. Applied Psychological Measurement, 42(5), 376–392.

    Article  Google Scholar 

  • Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic measurement: Theory, methods, and applications. New York, NY: Guilford Press.

    Google Scholar 

  • Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores (Psychometrika Monograph Supplement, No. 17).

    Google Scholar 

  • Tienken, C. H., & Wilson, M. J. (2007). The impact of computer assisted instruction on seventh-grade students’ mathematics achievement. Planning and Changing, 38, 181–190.

    Google Scholar 

  • Vermunt, J. K., & Magidson, J. (2013). Technical guide for latent GOLD 5.0: Basic, advanced, and syntax. Belmont, MA: Statistical Innovations, Inc.

    Google Scholar 

  • von Davier, M. (2005). A general diagnostic model applied to language testing data (Research Report RR-05-16). Princeton, NJ: ETS.

    Google Scholar 

  • von Davier, M. (2007). Mixture general diagnostic models (Research Report, RR-07-32). Princeton, NJ: ETS.

    Google Scholar 

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

    Article  Google Scholar 

  • von Davier, M. (2010). Hierarchical mixtures of diagnostic models. Psychological Test and Assessment Modeling, 52(1), 8–28.

    Google Scholar 

  • von Davier, M. (2014). The DINA model as a constrained general diagnostic model: Two variants of a model equivalency. British Journal of Mathematical and Statistical Psychology, 67, 49–71.

    Article  Google Scholar 

  • von Davier, M., Xu, X., & Carstensen, C. H. (2011). Measuring growth in a longitudinal large scale assessment with a general latent variable model. Psychometrika, 76(2), 318–336.

    Article  Google Scholar 

  • Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic model to NAEP data (RR-08-27, ETS Research Report).

    Google Scholar 

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Correspondence to Yoon Soo Park .

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Park, Y.S., Lee, YS. (2019). Explanatory 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_10

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  • DOI: https://doi.org/10.1007/978-3-030-05584-4_10

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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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