Evaluation of the Linear Composite Conjecture for Unidimensional IRT Scale for Multidimensional Responses

Area of Science:

• Psychometrics
• Educational Measurement
• Latent Variable Modeling

Background:

• The linear composite direction theoretically aligns unidimensional scales within multidimensional latent spaces.
• Compensatory multidimensional item response theory (IRT) models can derive this linear composite.

Purpose of the Study:

• To evaluate the validity of the linear composite conjecture.
• To assess the approximation accuracy of a unidimensional IRT model for the linear composite direction in multidimensional latent spaces.

Main Methods:

• Simulation experiments were conducted to analyze the approximation under varying conditions.
• A real data experiment utilized items from the American College Testing mathematics test.

Main Results:

• The unidimensional IRT model sufficiently approximates the linear composite direction when latent variables exhibit positive correlations.
• Instability arises when approximating the linear composite direction using a unidimensional IRT model with negatively correlated latent variables.

Conclusions:

• The unidimensional IRT model's utility in approximating the linear composite direction is contingent on the correlation between latent variables.
• Careful consideration of latent variable correlations is crucial when applying unidimensional IRT models in multidimensional contexts.