The Reliability of Diagnosing Broad and Narrow Skills in Middle School Mathematics with the Multicomponent Latent Trait Model

  • Susan EmbretsonEmail author
  • Kristin Morrison
  • Hea Won Jun
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 140)


The multicomponent latent trait model for diagnosis (MLTM-D;Embretson and Yang, Psychometrika 78:14–36, 2013) is a conjunctive item response model that is hierarchically organized to include broad and narrow skills. A two-stage adaptive testing procedure was applied to diagnose skill mastery in middle school mathematics and then analyzed with MLTM-D. Strong support for the reliability of diagnosing both broad and narrow skills was obtained from both stages of testing using decision confidence indices.


Diagnostic models Item response theory Multidimensional models Decision confidence reliability 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Susan Embretson
    • 1
    Email author
  • Kristin Morrison
    • 1
  • Hea Won Jun
    • 1
  1. 1.Georgia Institute of TechnologyAtlantaUSA

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