Abstract
The Reduced Reparameterized Unified Model (Reduced RUM) has received considerable attention among educational researchers. Markov chain Monte Carlo (MCMC) or Expectation Maximization (EM) is typically used for estimating the Reduced RUM. Implementations of the EM algorithm are available in the latent class analysis (LCA) routines of commercial software packages (e.g., Latent GOLD, Mplus). Using a commercial LCA routine as a vehicle for fitting the Reduced RUM with the EM algorithm requires that it be reparameterized as a logit model, with complex constraints imposed on the parameters. This article summarizes the general parameterization of the Reduced RUM as a logit model and the associated parameter constraints.
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References
C.-Y. Chiu, H.-F. Köhn, The reduced RUM as a logit model: parameterization and constraints. Psychometrika 81, 350–370 (2016)
C.-Y. Chiu, H.-F. Köhn, H.M. Wu, Fitting the reduced RUM using Mplus: a tutorial. Int. J. Test. 16, 331–351 (2016)
L.V. DiBello, L.A. Roussos, W.F. Stout, Review of cognitively diagnostic assessment and a summary of psychometric models, in Handbook of Statistics, ed. by C.R. Rao, S. Sinharay. Psychometrics, vol. 26. (Elsevier, Amsterdam, 2007), pp. 979–1030
Y. Feng, B.T. Habing, A. Huebner, Parameter estimation of the reduced RUM using the EM algorithm. Appl. Psychol. Meas. 38, 137–150 (2014)
S.J. Haberman, M. von Davier, Some notes on models for cognitively based skill diagnosis, in Handbook of Statistics, ed. by C.R. Rao, S. Sinharay. Psychometrics, vol. 26 (Elsevier, Amsterdam, 2007), pp. 1031–1038
S.M. Hartz, A Bayesian framework for the Unified Model for assessing cognitive abilities: Blending theory with practicality. Doctoral dissertation. Available from ProQuest Dissertations and Theses database. (UMI No. 3044108), 2002
S.M. Hartz, L.A. Roussos, The Fusion Model for skill diagnosis: Blending theory with practicality. (Research report No. RR-08-71), Educational Testing Service, Princeton, NJ, October 2008
R. Henson, J. Douglas, Test construction for cognitive diagnosis. Appl. Psychol. Meas. 29, 262–277 (2005)
R.A. Henson, J. Templin, Large-scale language assessment using cognitive diagnosis models. Paper presented at the Annual Meeting of the National Council on Measurement in Education, Chicago, IL, April 2007
R. Henson, J.L. Templin, J. Douglas, Using efficient model based sum-scores for conducting skills diagnoses. J. Educ. Meas. 44, 361–376 (2007)
R.A. Henson, J.L. Templin, J.T. Willse, Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika 74, 191–210 (2009)
R. Henson, L.A. Roussos, J. Douglas, X. He, Cognitive diagnostic skill-level discrimination indices. Appl. Psychol. Meas. 32, 275–288 (2008)
B.W. Junker, K. Sijtsma, Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Appl. Psychol. Meas. 25, 258–272 (2001)
Y.-H. Kim, Diagnosing EAP writing ability using the Reduced Reparameterized Unified Model. Lang. Test. 28, 509–541 (2011)
J. Leighton, M. Gierl, Cognitive Diagnostic Assessment for Education: Theory and Applications. (Cambridge University Press, Cambridge, 2007)
Y. Liu, J.A. Douglas, R.A. Henson, Testing person fit in cognitive diagnosis. Appl. Psychol. Meas. 33, 579–598 (2009)
G.B. Macready, C.M. Dayton, The use of probabilistic models in the assessment of mastery. J. Educ. Stat. 33, 379–416 (1977)
L.K. Muthén, B.O. Muthén, Mplus User’s Guide, 7th edn. (Muthén & Muthén, Los Angeles, 1998–2015)
A.A. Rupp, J.L. Templin, R.A. Henson, Diagnostic Measurement. Theory, Methods, and Applications (Guilford, New York, 2010)
J.L. Templin, R.A. Henson, S.E. Templin, L.A. Roussos, Robustness of hierarchical modeling of skill association in cognitive diagnosis models. Appl. Psychol. Meas. 32, 559–574 (2008)
J.K. Vermunt, J. Magidson, Latent GOLD 4.0 Users’s Guide (Statistical Innovations Inc., Belmont, 2005)
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Köhn, HF. (2017). Parameter Constraints of the Logit Form of the Reduced RUM. In: van der Ark, L.A., Wiberg, M., Culpepper, S.A., Douglas, J.A., Wang, WC. (eds) Quantitative Psychology. IMPS 2016. Springer Proceedings in Mathematics & Statistics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-319-56294-0_19
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DOI: https://doi.org/10.1007/978-3-319-56294-0_19
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