A Generalized Definition of Multidimensional Item Response Theory Parameters.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Standard multidimensional two-parameter logistic models have limitations in representing complex latent structures and item characteristics.
• Existing models may not fully capture non-identity latent covariances or negatively keyed items, impacting measurement accuracy.

Purpose of the Study:

• To generalize multidimensional discrimination and difficulty parameters within the multidimensional two-parameter logistic model.
• To incorporate non-identity latent covariances and negatively keyed items into IRT parameter definitions.
• To provide a geometrical representation of the measured construct and item properties in a distinct test space.

Main Methods:

• Generalization of multidimensional parameters using Reckase's maximum discrimination point method.
• Definition of parameters based on item parameters, latent covariance structure, and latent correlation structure.
• Development of a procedure for geometrical representation of items in a test space.

Main Results:

• Three versions of the generalized parameters were developed: item-based, covariance-based, and correlation-based.
• Items require representation in a test space, distinct from the latent space, for accurate measurement.
• The study provides a method for geometrical item representation and applies it to literature examples.

Conclusions:

• The generalized parameters offer a more accurate representation of item measurement properties.
• The covariance structure version is recommended for parameter property descriptions, while the correlation structure version is suitable for graphical representation.
• The generalization has implications for other multidimensional IRT models and parallels in common factor model theory.