Assessing Fit of Item Response Models Using the Information Matrix 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 versi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of educational measurement 2012-09, Vol.49 (3), p.247-268
Main Authors: Ranger, Jochen, Kuhn, Jörg-Tobias
Format: Article
Language:English
Subjects:
Calibration
Datasets
Degrees of freedom
Economic models
Educational evaluation
Equality
Expectation
Goodness of Fit
Hessian matrices
Identity
Information
Item Response Theory
Mathematical models
Matrices
Matrix
Modeling
Parametric models
Power
Simulation
Simulations
Statistical Analysis
Statistics
Test Items
Violations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 S — X² 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.
ISSN:0022-0655
1745-3984
DOI:10.1111/j.1745-3984.2012.00174.x