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Stabilizing Conditional Standard Errors of Measurement in Scale Score Transformations
Author(s) -
Moses Tim,
Kim YoungKoung
Publication year - 2017
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12140
Subject(s) - transformation (genetics) , scale (ratio) , variance (accounting) , standard error , econometrics , statistics , mathematics , scaling , standard deviation , binomial (polynomial) , binomial distribution , computer science , economics , physics , quantum mechanics , biochemistry , chemistry , accounting , geometry , gene
The focus of this article is on scale score transformations that can be used to stabilize conditional standard errors of measurement (CSEMs). Three transformations for stabilizing the estimated CSEMs are reviewed, including the traditional arcsine transformation, a recently developed general variance stabilization transformation, and a new method proposed in this article involving cubic transformations. Two examples are provided and the three scale score transformations are compared in terms of how well they stabilize CSEMs estimated from compound binomial and item response theory (IRT) models. Advantages of the cubic transformation are demonstrated with respect to CSEM stabilization and other scaling criteria (e.g., scale score distributions that are more symmetric).