Local minima and factor rotations in exploratory factor analysis.

Area of Science:

• Psychometrics
• Statistical Analysis
• Data Science

Background:

• Exploratory factor analysis (EFA) relies on factor rotation algorithms.
• These algorithms may converge to local solutions (minima), impacting results.
• Understanding the prevalence and causes of local solutions is crucial for reliable analysis.

Purpose of the Study:

• Investigate the frequency and correlates of local solutions in EFA.
• Evaluate the performance of five common factor rotation algorithms.
• Determine factors influencing the occurrence of local solutions.

Main Methods:

• Simulated 16,000 datasets and performed over 57 million factor rotations.
• Tested five algorithms: varimax, oblimin, entropy, and geomin (orthogonal/oblique).
• Examined effects of factor loading size, indicators, cross-loadings, sample size, and model error.

Main Results:

• All tested algorithms converged to local solutions under certain conditions.
• Geomin (orthogonal and oblique) algorithms produced the highest number of local solutions.
• Maximum hyperplane count was a better indicator of the population factor pattern than minimum complexity.

Conclusions:

• Local solutions are a common issue in factor rotation across various algorithms.
• Algorithm choice and data characteristics influence the likelihood of encountering local solutions.
• The maximum hyperplane count criterion is recommended for selecting the best factor pattern when multiple solutions arise.