A Comprehensive IRT Approach for Modeling Binary, Graded, and Continuous Responses With Error in Persons and Items

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Existing dual item response theory (IRT) models are limited to continuous response data.
• A need exists for flexible IRT models accommodating diverse response formats and differential measurement error.
• Previous advancements in dual IRT models have not addressed graded or binary response types.

Purpose of the Study:

• To develop a comprehensive dual modeling approach for item response theory (IRT) based on latent response variables.
• To extend dual IRT modeling to accommodate continuous, graded, and binary response data.
• To provide procedures for item calibration, individual scoring, model fit assessment, and measurement precision evaluation within the proposed framework.

Main Methods:

• A unified dual modeling approach is presented, grounded in underlying latent response variables.
• Specific models for continuous, graded, and binary responses are derived from the general framework.
• Procedures for item calibration, individual scoring, model appropriateness assessment, and measurement precision evaluation are discussed.

Main Results:

• Simulation studies indicate the proposed dual modeling approach is feasible and effective across different response types.
• The framework successfully integrates models for continuous, graded, and binary data.
• Empirical illustration in the personality domain demonstrates practical applicability.

Conclusions:

• The developed comprehensive dual modeling approach offers a flexible and unified framework for item response theory (IRT).
• This approach extends the utility of dual IRT models to a wider range of data types, enhancing measurement capabilities.
• The methodology provides robust procedures for psychometric analysis and is practically demonstrated.