On Lagrange Multiplier Tests in Multidimensional Item Response Theory: Information Matrices and Model Misspecification

Educational and Psychological Measurement
Carl F Falk, Scott Monroe

Abstract

Lagrange multiplier (LM) or score tests have seen renewed interest for the purpose of diagnosing misspecification in item response theory (IRT) models. LM tests can also be used to test whether parameters differ from a fixed value. We argue that the utility of LM tests depends on both the method used to compute the test and the degree of misspecification in the initially fitted model. We demonstrate both of these points in the context of a multidimensional IRT framework. Through an extensive Monte Carlo simulation study, we examine the performance of LM tests under varying degrees of model misspecification, model size, and different information matrix approximations. A generalized LM test designed specifically for use under misspecification, which has apparently not been previously studied in an IRT framework, performed the best in our simulations. Finally, we reemphasize caution in using LM tests for model specification searches.

References

Nov 1, 2007·The British Journal of Mathematical and Statistical Psychology·Li Cai
Sep 2, 2009·Psychological Methods·Carlos G Forero, Alberto Maydeu-Olivares
Jul 20, 2010·Psychometrika·Albert Satorra, Peter M Bentler
Mar 25, 2014·Psychometrika·Ke-Hai YuanJeff Patton
Oct 7, 2014·The British Journal of Mathematical and Statistical Psychology·Yang Liu, David Thissen
Jan 1, 2003·Multivariate Behavioral Research·Robert C MacCallum
Mar 1, 2006·Multivariate Behavioral Research·Albert Maydeu-Olivares, Li Cai

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Citations

Mar 3, 2020·Frontiers in Psychology·Jochen Ranger, Sören Much
Oct 27, 2020·Multivariate Behavioral Research·Joshua StarrDavid D Vachon

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Software Mentioned

IRT
custom
R
R R Core Team
flexMIRT

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