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

Carl F Falk¹, Scott Monroe²

¹Michigan State University, East Lansing, MI, USA.

Educational and Psychological Measurement

|August 28, 2018

Summary

Lagrange multiplier (LM) tests are useful for diagnosing item response theory (IRT) model misspecification. A generalized LM test performed best in simulations, but caution is still advised for model specification searches.

Keywords:

Lagrange multiplier test modification indices multidimensional item response theory score test

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Area of Science:

Psychometrics
Statistical Modeling

Background:

Lagrange multiplier (LM) tests, also known as score tests, are increasingly used for diagnosing misspecification in item response theory (IRT) models.
These tests can also assess if model parameters deviate from a fixed value.

Purpose of the Study:

To investigate the utility of LM tests for diagnosing misspecification in multidimensional IRT models.
To evaluate the impact of computation methods and the degree of misspecification on LM test performance.

Main Methods:

An extensive Monte Carlo simulation study was conducted within a multidimensional IRT framework.
The study examined LM test performance under varying degrees of model misspecification, model size, and different information matrix approximations.

Main Results:

The utility of LM tests is contingent upon the computation method and the extent of initial model misspecification.
A generalized LM test, specifically adapted for use under misspecification and not previously studied in IRT, demonstrated superior performance in simulations.

Conclusions:

The findings highlight the importance of selecting appropriate LM test computation methods.
While a generalized LM test shows promise, continued caution is recommended when employing LM tests for model specification searches in IRT.