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A Multicomponent Latent Trait Model for Diagnosis

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  • Susan Embretson
  • Xiangdong Yang

Abstract

This paper presents a noncompensatory latent trait model, the multicomponent latent trait model for diagnosis (MLTM-D), for cognitive diagnosis. In MLTM-D, a hierarchical relationship between components and attributes is specified to be applicable to permit diagnosis at two levels. MLTM-D is a generalization of the multicomponent latent trait model (MLTM; Whitely in Psychometrika, 45:479–494, 1980 ; Embretson in Psychometrika, 49:175–186, 1984 ) to be applicable to measures of broad traits, such as achievement tests, in which component structure varies between items. Conditions for model identification are described and marginal maximum likelihood estimators are presented, along with simulation data to demonstrate parameter recovery. To illustrate how MLTM-D can be used for diagnosis, an application to a large-scale test of mathematics achievement is presented. An advantage of MLTM-D for diagnosis is that it may be more applicable to large-scale assessments with more heterogeneous items than are latent class models. Copyright The Psychometric Society 2013

Suggested Citation

  • Susan Embretson & Xiangdong Yang, 2013. "A Multicomponent Latent Trait Model for Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 14-36, January.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:1:p:14-36
    DOI: 10.1007/s11336-012-9296-y
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Cho, S.-J. & Rabe-Hesketh, S., 2011. "Alternating imputation posterior estimation of models with crossed random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 12-25, January.
    3. Jimmy Torre & Jeffrey Douglas, 2004. "Higher-order latent trait models for cognitive diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 333-353, September.
    4. Susan Embretson, 1999. "Generating items during testing: Psychometric issues and models," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 407-433, December.
    5. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    6. Susan Whitely, 1980. "Multicomponent latent trait models for ability tests," Psychometrika, Springer;The Psychometric Society, vol. 45(4), pages 479-494, December.
    7. Susan Embretson (Whitely), 1984. "A general latent trait model for response processes," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 175-186, June.
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    Cited by:

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    2. Chun Wang, 2021. "Using Penalized EM Algorithm to Infer Learning Trajectories in Latent Transition CDM," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 167-189, March.

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