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A functional approach of item response estimation and its application in
polytomous item analysis and differential
item functioning (DIF) analysis are discussed in the paper.
These estimators can capture the unique features of psychology item
which are erased by current nonparametric and parametric models. In addition, the visual plots provide more information than the traditional methods for analyzing item behaviors.
A personality assessment is used to illustrate the application.
It is recommended to use the functional DIF approach to supplement the traditional DIF methods, such as the Mantel-Haenszel DIF analyzes, to
obtain a full picture of the behavior of a psychology item.