Mixture IRT Model With a Higher-Order Structure for Latent Traits.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Mixture item response theory (IRT) models are useful for detecting latent classes in test development.
• Higher-order structures of multiple latent traits can influence examinee response patterns.
• Existing models may not fully capture the complexity of higher-order latent class mixtures.

Purpose of the Study:

• To develop novel higher-order mixture IRT models integrating mixture and higher-order IRT concepts.
• To accommodate both linear and nonlinear latent trait models with various item response functions.
• To address practical concerns in testing situations involving complex latent structures.

Main Methods:

• Development of higher-order mixture IRT models.
• Application of Rasch model and multiparameter IRT models in simulation studies.
• Bayesian estimation using WinBUGS software.
• Simulation studies with varying sample sizes and test lengths.
• Comparison of linear and nonlinear latent trait models.
• Analysis of mixture bifactor models.

Main Results:

• Bayesian estimation in WinBUGS demonstrated good parameter recovery.
• Larger sample sizes improved model parameter estimation.
• Longer test lengths enhanced individual ability and latent class membership recovery.
• Linear approach superior for first-order latent traits; nonlinear approach superior for second-order traits.
• Mixture bifactor model fitting led to biased estimates when factor loadings were constrained.

Conclusions:

• The proposed higher-order mixture IRT models provide a robust framework for analyzing complex latent structures.
• Model performance is influenced by sample size, test length, and the chosen latent trait model (linear/nonlinear).
• Careful consideration of model specification, such as factor loadings in bifactor models, is crucial for accurate estimation.