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Assessing Fit of Item Response Models Using the Information Matrix Test
Author(s) -
Ranger Jochen,
Kuhn JörgTobias
Publication year - 2012
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/j.1745-3984.2012.00174.x
Subject(s) - hessian matrix , test (biology) , mathematics , independence (probability theory) , matrix (chemical analysis) , item response theory , statistics , identity matrix , fisher information , type i and type ii errors , test score , psychometrics , eigenvalues and eigenvectors , paleontology , materials science , physics , quantum mechanics , composite material , biology , standardized test
The information matrix can equivalently be determined via the expectation of the Hessian matrix or the expectation of the outer product of the score vector. The identity of these two matrices, however, is only valid in case of a correctly specified model. Therefore, differences between the two versions of the observed information matrix indicate model misfit. The equality of both matrices can be tested with the so‐called information matrix test as a general test of misspecification. This test can be adapted to item response models in order to evaluate the fit of single items and the fit of the whole scale. The performance of different versions of the test is compared in a simulation study with existing tests of model fit, among them the test of Orlando and Thissen, the score test of local independence due to Glas and Suarez‐Falcon, and the limited information approach of Maydeu‐Olivares and Joe. In general, the different versions of the information matrix test adhere to the nominal Type I error rate and have high power for detecting misspecified item characteristic curves. Additionally, some versions of the test can be used in order to detect violations of the local independence assumption.