A Multidimensional Item Response Theory Model for Continuous and Graded Responses With Error in Persons and Items

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Item response theory (IRT) dual models (DMs) account for measurement error from both items and individuals.
• Existing DMs are limited to unidimensional measures, restricting their application in complex assessments.

Purpose of the Study:

• To propose and describe two multidimensional extensions of dual models (DMs) for IRT.
• To provide a framework for calibrating items, scoring individuals, and assessing model fit and precision in multidimensional contexts.

Main Methods:

• Development of the multidimensional dual Thurstonian continuous response model (M-DTCRM) for continuous responses.
• Development of the multidimensional dual Thurstonian graded response model (M-DTGRM) for ordered-categorical responses.
• Utilizing factor-analytic and IRT parameterizations, supported by simulation studies.

Main Results:

• The proposed multidimensional dual models (M-DTCRM and M-DTGRM) are shown to be feasible through simulation.
• The models offer a viable solution for multidimensional questionnaires with insufficient items per scale.

Conclusions:

• The developed multidimensional dual models extend the utility of IRT for complex, multi-construct assessments.
• These models enhance measurement precision and estimation stability in scenarios where unidimensional approaches are inadequate.