A Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model

Glas, Cees A.W. and Suarez Falcon, Juan Carlos (2003) A Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model. Applied Psychological Measurement, 27 (2). pp. 87-106. ISSN 0146-6216

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Abstract:	In this article, the Type I error rate and the power of a number of existing and new tests of fit to the 3-parameter logistic model (3PLM) are investigated. The first test is a generalization of a test for the evaluation of the fit to the 2-parameter logistic model (2PLM) based on the Lagrange multiplier (LM) test or the equivalent efficient score test. This technique is applied to two model violations: deviation from the 3PLM item characteristic curve and violation of local stochastic independence. The LM test for the first violation is compared with the Q1 – G²j and S – G²j tests, respectively. The LM test for the second violation is compared with the Q3 test and a new test, the S3 test, which can be viewed as a generalization of the approach of the S – G²j test to the evaluation of violation of local independence. The results of simulation studies indicate that all tests, except the Q1 – G²j test, have a Type I error rate that is acceptably close to the nominal significance level, and good power to detect the model violations they are targeted at. When, however, misfitting items are present in a test, the proportion of items that are flagged incorrectly as misfitting can become undesirably high, especially for short tests.
Item Type:	Article
Copyright:	© 2003 Sage
Faculty:	Behavioural Sciences (BS)
Research Group:	Research Methodology, Measurement and Data Analysis (OMD)
Link to this item:	http://purl.utwente.nl/publications/60161
Official URL:	http://dx.doi.org/10.1177/0146621602250530
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