Model Fit with Residual Analyses

Authored by: Craig S. Wells , Ronald K. Hambleton

Handbook of Item Response Theory Volume Two Statistical Tools

Print publication date:  February  2016
Online publication date:  March  2017

Print ISBN: 9781466514324
eBook ISBN: 9781315373645
Adobe ISBN:


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Item response theory (IRT) is a powerful scaling technique that uses a mathematical model to depict the probability of a correct response given item and person parameters. The advantages and attractive features of IRT are based on the invariance property in which the item parameter values retain the same values regardless of the ability distribution and the person parameters (Embretson and Reise, 2000; Hambleton et al., 1991). However, the invariance property only holds when the assumptions of the specific IRT model, such as undimensionality, local independence, and monotonicity l (Volume One, Chapter 2) are satisfied. Model fit, which is the focus of this chapter, indicates that these assumptions adequately match or represent the examinee response data.

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