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Monotone Properties of a General Diagnostic Model GDM MLR

Xu, Xueli
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
General Diagnostic Model (GDM), Latent Trait Theory, Monotone Likelihood Ratio (MLR)


Monotonicity properties of a general diagnostic model (GDM) are considered in this paper. Simple data summaries are identified to inform about the ordered categories of latent traits. The findings are very much in accordance with the statements made about GPCM (Hemker, Sijtsma, Molenaar, & Junker, 1996, 1997). On the one hand, by fitting a GDM with equal slopes across items, the observed total score [un-reproducible equation] demonstrates the monotone likelihood ratio (MLR) property in individual coordinate at the cost of losing model fit. On the other hand, fitting a GDM without slope restriction increases the model fit but by sacrificing MLR property. Trade-offs between these two situations should be considered in practice.

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