A simple approach to guide factor retention decisions when applying principal component analysis to biomechanical...

Area of Science:

• Biomechanics
• Multivariate Statistics
• Data Analysis

Background:

• Principal Component Analysis (PCA) is increasingly used for biomechanical data reduction.
• A lack of standardized criteria for determining the number of principal components (factors) to retain complicates data interpretation and comparison across studies.

Purpose of the Study:

• To present power equations that support the use of Parallel Analysis (PA) as a criterion for principal component (PC) retention.
• To offer a quantitative and transparent method for deciding how many factors to retain during PCA in biomechanics.

Main Methods:

• Monte Carlo simulations were employed to perform PCA on random datasets of varying dimensions.
• The simulations mimicked the PA procedure to determine PC retention criteria.
• Power relationships were fitted to surfaces plotting PA outcomes against dataset dimensions.

Main Results:

• Power equations were derived to predict the expected outcome of PA based on dataset dimensions.
• Coefficients for these equations are reported, enabling prediction of PA outcomes.
• The study provides a method to determine PC retention for datasets within the tested dimensional range.

Conclusions:

• The developed power equations facilitate the adoption of PA as a standard criterion for PC retention.
• Implementing PA offers a transparent and quantifiable approach to factor retention in PCA.
• This standardization will improve the comparability and contrastability of findings across biomechanical studies.