Generation and Objective Rotation of Generalized Learning Curves Using Matrix Language Products

Area of Science:

• Psychometrics
• Quantitative Psychology
• Data Analysis

Background:

• Principal components analysis is a common technique for data reduction.
• Generalized learning curves are used to model performance changes over time.
• Objective rotation of components is crucial for interpretable results, but often challenging.

Purpose of the Study:

• To present SAS macros for Tucker's modified principal components approach to generalized learning curves analysis.
• To address the challenge of rotating components to achieve psychologically meaningful solutions.
• To provide researchers with tools for objective rotation and factor score generation.

Main Methods:

• Development and application of two SAS macros for Tucker's modified principal components analysis.
• Implementation of matrix manipulation for objective component rotation.
• Description of three additional SAS macros for dimension reflection, objective rotation, and factor score generation.

Main Results:

• The presented SAS macros facilitate Tucker's modified principal components analysis for generalized learning curves.
• Objective rotation of components is achieved, aligning with Tucker's desiderata.
• The macros enable the generation of interpretable factor scores from rotated solutions.

Conclusions:

• The SAS macros offer a valuable tool for researchers analyzing generalized learning curves.
• Objective rotation simplifies the interpretation of psychological meaningfulness in component analysis.
• These tools enhance the rigor and efficiency of learning curve modeling.