Cognitive diagnosis models for baseline testing of educational standards in math

References

• H. Akaike, A new look at the statistical model identification, IEEE Trans. Autom. Control 19 (1974), pp. 716–723. doi: 10.1109/TAC.1974.1100705
   Web of Science ®Google Scholar
• M. Birenbaum, C. Tatsuoka, and Y. Yamada, Diagnostic assessment in TIMMS-R: Between countries and within country comparisons of eighth graders’ mathematics performance, Stud. Educ. Eval. 30 (2004), pp. 151–173.
   Google Scholar
• W. Bos, S. Hornberg, K. Arnold, G. Faust, L. Fried, E. Lankes, K. Schwippert, and R. Valtin, (eds.), IGLU 2006: Lesekompentenzen von Grundschülern in Deutschland im internationalen Vergleich, Waxmann, Münster, 2007.
   Google Scholar
• S. Breit and C. Schreiner, Bildungsstandards: Baseline 2009 (8. Schulstufe), Tech. Rep., Bundesinstitut für Innovation und Entwicklung des österreichischen Schulwesens, Salzburg, Austria, 2010.
   Google Scholar
• J. Chen and J. de la Torre, A general cognitive diagnosis model for expert-defined polytomous attributes, Appl. Psycholog. Meas. (2013), pp. 419–437. doi: 10.1177/0146621613479818
   Web of Science ®Google Scholar
• J. Chen, J. de la Torre, and Z. Zhang, Relative and absolute fit evaluation in cognitive diagnosis modeling, Journal of Educ. Meas. 50 (2013), pp. 123–140. doi: 10.1111/j.1745-3984.2012.00185.x
   Web of Science ®Google Scholar
• C.-Y. Chiu, J.A. Douglas, and X. Li, Cluster Analysis for Cognitive Diagnosis: Theory and Applications, Psychometrika 74 (2009), pp. 633–665. doi: 10.1007/s11336-009-9125-0
   Web of Science ®Google Scholar
• J. de la Torre, An empirically based method of Q-matrix validation for the DINA model: Development and applications, J. Educ. Meas. 45 (2008), pp. 343–362. doi: 10.1111/j.1745-3984.2008.00069.x
   Web of Science ®Google Scholar
• J. de la Torre, DINA model parameter estimation: A didactic, J. Educ. Behav. Stat. 34 (2009), pp. 115–130. doi: 10.3102/1076998607309474
   Web of Science ®Google Scholar
• J. de la Torre, The generalized DINA model framework, Psychometrika 76 (2011), pp. 179–199. doi: 10.1007/s11336-011-9207-7
   Web of Science ®Google Scholar
• J. de la Torre and J.A. Douglas, Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data, Psychometrika 73 (2008), pp. 595–624. doi: 10.1007/s11336-008-9063-2
   Web of Science ®Google Scholar
• S. Embretson, A general latent trait model for response processes, Psychometrika 49 (1984), pp. 175–186. doi: 10.1007/BF02294171
   Web of Science ®Google Scholar
• J. Groß and A. George, On permissible attribute classes in noncompensatory cognitive diagnosis models, Methodology 10 (2014), pp. 100–107.
   Web of Science ®Google Scholar
• H. Haertel, Using restricted latent class models to map the skill structure of achievement items, J. Educ. Meas. 26 (1989), pp. 333–352. doi: 10.1111/j.1745-3984.1989.tb00336.x
   Web of Science ®Google Scholar
• A. Huebner and C. Wang, A note on comparing examinee classification methods for cognitive diagnosis models, Educ. Psycholog. Meas. 71 (2011), pp. 407–419. doi: 10.1177/0013164410388832
   Web of Science ®Google Scholar
• Y. Huo and J. de la Torre, Estimating a cognitive diagnostic model for multiple strategies via the em algorithm, Appl. Psycholog. Meas. (2014), pp. 464–485. doi: 10.1177/0146621614533986
   Web of Science ®Google Scholar
• B.W. Junker and K. Sijtsma, Cognitive assessment models with few assumptions, and connections with nonparametric item response theory, Appl. Psycholog. Meas. 25 (2001), pp. 258–272. doi: 10.1177/01466210122032064
   Web of Science ®Google Scholar
• T. Karelitz, Ordered category attribute coding framework for cognitive assessments, 2004. Unpublished doctoral dissertation. University of Illinois at Urbana-Champaign.
   Google Scholar
• O. Kunina-Habenicht, A.A. Rupp, and O. Wilhelm, A practical illustration of multidimensional diagnostic skills profiling: Comparing results from confirmatory factor analysis and diagnostic classification models, Stud. Educ. Eval. 35 (2009), pp. 64–70. doi: 10.1016/j.stueduc.2009.10.003
   Google Scholar
• Y.S. Lee, J. de la Torre, and Y.S. Park, Relationships between cognitive diagnosis, CTT, and IRT indices: an empirical investigation, Asia Pacific Educ. Rev, 13 (2012), pp. 333–345. doi: 10.1007/s12564-011-9196-3
   Web of Science ®Google Scholar
• E. Maris, Psychometric latent response models, Psychometrika 60 (1995), pp. 523–547. doi: 10.1007/BF02294327
   Web of Science ®Google Scholar
• I. Mullis, M. Martin, G. Ruddock, C. O'Sullivan, A. Arora, and E. Erberber, TIMSS 2007 Assessment Frameworks, TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, 2005.
   Google Scholar
• U. Olsson, Maximum likelihood estimation of the polychoric correlation coefficient, Psychometrika 44 (1979), pp. 443–460. doi: 10.1007/BF02296207
   Web of Science ®Google Scholar
• C. Park and D. Bolt, Application of multilevel IRT to investigate cross-national skill profiles on TIMSS 2003, in IERI Monograph Series: Issues and Methodologies in Large-Scale Assessments, M.von Davier and D. Hastedt, eds., Vol. 1, Educational Testing Service and International Association for the Evaluation of Educational Achievement, IERI, 2008, pp. 71–96.
   Google Scholar
• Y. Park and Y.S. Lee, Diagnostic cluster analysis of mathematical skills, in IERI Monograph Series: Issues and Methodologies in Large-Scale Assessments, M. von Davier and D. Hastedt, eds., Vol. 4, Educational Testing Service and International Association for the Evaluation of Educational Achievement, IERI, 2011, pp. 75–107.
   Google Scholar
• W. Peschek and H. Heugl, Standards für die mathematischen Fähigkeiten österreichischer Schülerinnen und Schüler am Ende der 8. Schulstufe, Tech. Rep., Alpen-Adria-University Klagenfurt, Klagenfurt, Austria, 2007.
   Google Scholar
• R Core Team, R: A language and environment for statistical computing (2014), Available at http://www.R-project.org.
   Google Scholar
• A. Robitzsch, T. Kiefer, A. George, and A. Ünlü, CDM: Cognitive diagnosis modeling (2014), http://CRAN.R-project.org/package=CDM, R package version 3.4-21.
   Google Scholar
• A. Rupp, J. Templin, and R. Henson, Diagnostic Measurement. Theory, Methods, and Applications, The Guildford Press, New York, 2010.
   Google Scholar
• G. Schwarz, Estimating the dimension of a model, Ann. Stat. 6 (1978), pp. 461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• K.K. Tatsuoka, Rule space: An approach for dealing with misconceptions based on item response theory, J. Educ. Meas, 20 (1983), pp. 345–354. doi: 10.1111/j.1745-3984.1983.tb00212.x
   Web of Science ®Google Scholar
• K. Tatsuoka, Toward an integration of item-response theory and cognitive error diagnosis, Diagnostic Monitoring of Skill and Knowledge Acquisition, N. Frederiksen, R. Glaser, A. Lesgold, and M.G. Shafto, eds., Erlbaum, Hillsdale, NJ, 1990, pp. 453–488.
   Google Scholar
• K.K. Tatsuoka, J.E. Corter, and C. Tatsuoka, Patterns of diagnosed mathematical content and process skills in TIMSS-R across a sample of 20 countries, Am. Educ. Res. J. 41 (2004), pp. 901–926. doi: 10.3102/00028312041004901
   Web of Science ®Google Scholar
• M. von Davier, A general diagnostic model applied to language testing data, Br. J. Math. Statist. Psychol. 61 (2008), pp. 287–307. doi: 10.1348/000711007X193957
   PubMed Web of Science ®Google Scholar