General mixture item response models with different item response structures: Exposition with an application to...

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Item response theory (IRT) models often assume a single process underlies all responses.
• Violations of measurement invariance can complicate data interpretation.
• Existing IRT models may not adequately capture heterogeneity in response behaviors.

Purpose of the Study:

• To propose a general mixture item response theory (IRT) framework.
• To allow for distinct classes of individuals with differing item response processes.
• To address violations of measurement invariance by estimating nonnested IRT models for different classes.

Main Methods:

• Utilized mixture models to estimate separate IRT models for different person classes.
• Estimated class membership for each individual within the sample.
• Applied a two-class mixture model comparing a generalized partial credit model with an IRTree model for Likert-scale items.

Main Results:

• Demonstrated the framework's ability to accommodate nonnested IRT models.
• Showcased how the middle response category can be modeled differently (e.g., as endorsement vs. nonresponse).
• Validated the mixture model through simulation studies and an empirical application.

Conclusions:

• The proposed mixture IRT framework offers a flexible approach to modeling response heterogeneity.
• This method can help researchers manage violations of measurement invariance.
• The framework provides a powerful tool for analyzing complex survey and assessment data.