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