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The Hierarchy Misfit Index: Evaluating Person Fit for Cognitive Diagnostic Assessment Open Access


Other title
hierarchical misft index
cognitive diagnostic model
hierarchical consistency index
educational measurement
person fit index
attribute hierarchy method
Type of item
Degree grantor
University of Alberta
Author or creator
Guo, Qi
Supervisor and department
Leighton, Jacqueline (Educational Psychology)
Examining committee member and department
McGarvey, Lynn (Elementary Education)
Cui, Ying (Educational Psychology)
Department of Educational Psychology
Measurement, Evaluation and Cognition
Date accepted
Graduation date
Master of Education
Degree level
As cognitive diagnostic models (CDMs) become increasingly popular in modern educational measurement, it is important to develop a person fit index that examines the appropriateness of a CDM for each individual examinee. The purpose of this study is to propose a new person fit index, the hierarchy misfit index (HMI), for CDMs, and test the power and type 1 error of the HMI at detecting misfitting item response vectors using a simulation study. The results of the simulation study showed that the HMI had high powers and acceptable type 1 errors when a test consisted of highly discriminating items. But when a test consisted of low discriminating items, the HMI’s type 1 errors were too high to be acceptable. A comparison was also made with a previously developed person fit index, the hierarchical consistency index, (HCI). The results showed that the HMI performed better in high item discrimination conditions.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Bloom B. S. (1956). Taxonomy of Educational Objectives, Handbook I: The Cognitive Domain. New York: David McKay Co Inc.Cui, Y., Leighton, J.P., Gierl, M.J., & Hunka, S. (2006). The hierarchical consistency index: a person-fit statistic for the attribute hierarchy method. Paper presented at the 2006 annual meeting of the National Council on Measurement in Education (NCME), San Francisco, CA.Cui, Y., and Leighton, J.P. (2009). The hierarchy consistency index: evaluating person fit for cognitive diagnostic assessment. Journal of Educational Measurement, 46(4), 429-449. doi: 10.1111/j.1745-3984.2009.00091.xEmbretson, S.E. (1984). A general latent trait model for response processes. Psychometrika, 49, 175-186. doi:10.1007/BF02294171Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research. Acta Pschologica, 37, 395-374. doi:10.1016/0001-6918(73)90003-6Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage Publications.Leighton, J. P., Gierl, M. J., & Hunka, S. M. (2004). The Attribute Hierarchy Method for Cognitive Assessment: A Variation on Tatsuoka's Rule-Space Approach. Journal of Educational Measurement, 41(3), 205-237. doi:10.1111/j.1745-3984.2004.tb01163.xLeighton, J. P., & Gierl, M. J. (Eds.) (2007). Cognitive diagnostic assessment for education: Theory and practices. Cambridge University Press.Leighton, J.P., & Gierl, M.J. (2011). The learning sciences in educational assessment: the role of cognitive models. New York, NY, US: Cambridge University Press.Meijer, R. R., & Sijtsma, K. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25, 107-135. doi:10.1177/01466210122031957Mislevy, R. J., Steinberg, L. & Almond, R. (2003). On the structure of educational assessments. Measurement: Interdisciplinary Research and Perspective. Hillsdale, NJ: Lawrence Erlbaum Associates.Mislevy, R. J. (2006). Cognitive psychology and educational assessment. In R. Brennan (Ed.), Educational Measurement (4th Ed.). Phoenix, AZ: Greenwood.Nichols, P.D. (1994). A framework for developing cognitively diagnostic assessment. Review of Educational Research, 64(4), 575-603. doi:10.3102/00346543064004575Piaget, J. (1983). "Piaget's Theory". In P. Mussen (Ed.) Handbook of child psychology. Wiley.Tatsuoka, K. K. (1984). Caution indices based on item response theory. Psychometrika, 49, 95-110. doi:10.1007/BF02294208

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