Latent class models for testing monotonicity and invariant item ordering for polytomous items.

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Item response theory (IRT) relies on assumptions like monotonicity (M) and invariant item ordering (IIO).
• Violations of M and IIO can compromise the validity of IRT-based inferences.
• Existing methods for assessing these assumptions may be limited.

Purpose of the Study:

• To propose a latent class model for ordinal items to test violations of M and IIO.
• To develop a statistical framework for assessing the integrity of IRT assumptions.
• To provide practical tools for identifying problematic items.

Main Methods:

• A latent class model with inequality constraints on class-specific item means was developed.
• Gibbs sampling was employed for parameter estimation.
• Deviance information criterion (DIC) and posterior predictive checks were used for assumption testing.

Main Results:

• The proposed latent class model effectively detects violations of M and IIO.
• DIC serves as an overall test for M and IIO.
• Posterior predictive checks allow for item-level assessment of these assumptions.

Conclusions:

• The developed latent class model is a valuable tool for assessing IRT assumption violations.
• The study offers a robust strategy for identifying items that violate M and IIO.
• This approach enhances the reliability of IRT applications in various fields.