Lord-Wingersky Algorithm Version 2.0 for Hierarchical Item Factor Models with Applications in Test Scoring, Scale...

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• The Lord-Wingersky recursive algorithm is effective for unidimensional item response theory (IRT).
• Extending this algorithm to multidimensional IRT (MIRT) increases computational complexity exponentially with dimensions.
• High-dimensional MIRT models pose significant computational challenges for existing algorithms.

Purpose of the Study:

• To develop a dimension reduction method specifically for the Lord-Wingersky recursions in MIRT.
• To reduce the computational burden of applying the Lord-Wingersky algorithm to high-dimensional IRT models.
• To enable new applications of the algorithm by overcoming computational limitations.

Main Methods:

• Developed a dimension reduction technique tailored to the Lord-Wingersky recursions.
• Leveraged restrictions from hierarchical item factor models (e.g., bifactor, testlet, two-tier models).
• Applied the algorithm on a reduced set of quadrature points, effectively lowering integration dimensions.

Main Results:

• The new method dramatically reduces the number of quadrature points required for high-dimensional models.
• In bifactor models, the effective dimension of integration is consistently reduced to 2.
• The algorithm facilitates the creation of accurate summed score to IRT scaled score translation tables, accounting for residual dependence.

Conclusions:

• The dimension reduction method makes the Lord-Wingersky algorithm practical for high-dimensional IRT models.
• This advancement enables novel applications in test scoring, linking, and model fit checking.
• The approach offers an efficient way to handle complex multidimensional IRT models.