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.
Original language | Undefined |
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Pages (from-to) | 81-100 |
Number of pages | 20 |
Journal | Applied psychological measurement |
Volume | 27 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2003 |
Keywords
- IR-60161
- METIS-215710
- modification indices
- item response theory (item fit)
- item fit
- efficient score test
- power studies
- three-parameter logistic model
- Lagrange multiplier test
- Type I error
- Goodness of Fit
- Chi-square distribution