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The Invariance of Latent and Observed Linking Functions in the Presence of Multiple Latent Test-Taker Dimensions

Dorans, Neil J.; Lin, Peng; Wang, Wei; Yao, Lili
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Report Number:
ETS Research Report
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Subject/Key Words:
Multidimensionality, Simple Structure, Invariance of Linking, Latent Variables, Observed Scores, Test Takers


This study examines linking relationships among latent test scores and how these latent linking relationships relate to observed-score linkings. Equations are used to describe the effects of correlation between underlying latent dimensions and the similarity or dissimilarity of test composition on linking functions among latent test scores. These equations describing relationships among latent test scores are used to model the results obtained from a previous simulation study, which illustrated that if the two tests have parallel structure then the linking relationship between their observed scores is subpopulation invariant regardless of the correlations between the underlying latent dimensions. The equations also model the effect that the degree of correlation between the latent dimensions has on equatability as the structure departs from parallelism.

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