A simple approach to guide factor retention decisions when applying principal component analysis to biomechanical data
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.025 | 0.140 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.005 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.022 | 0.010 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".