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

The use of principal component analysis (PCA) as a multivariate statistical approach to reduce complex biomechanical data-sets is growing. With its increased application in biomechanics, there has been a concurrent divergence in the use of criteria to determine how much the data is reduced (i.e. how many principal factors are retained). This short communication presents power equations to support the use of a parallel analysis (PA) criterion as a quantitative and transparent method for determining how many factors to retain when conducting a PCA. Monte Carlo simulation was used to carry out PCA on random data-sets of varying dimension. This process mimicked the PA procedure that would be required to determine principal component (PC) retention for any independent study in which the data-set dimensions fell within the range tested here. A surface was plotted for each of the first eight PCs, expressing the expected outcome of a PA as a function of the dimensions of a data-set. A power relationship was used to fit the surface, facilitating the prediction of the expected outcome of a PA as a function of the dimensions of a data-set. Coefficients used to fit the surface and facilitate prediction are reported. These equations enable the PA to be freely adopted as a criterion to inform PC retention. A transparent and quantifiable criterion to determine how many PCs to retain will enhance the ability to compare and contrast between studies.