GIVING MEANINGFUL INTERPRETATION TO ORDINATION AXES: ASSESSING LOADING SIGNIFICANCE IN PRINCIPAL COMPONENT ANALYSIS
Bibliographic record
Abstract
Principal component analysis (PCA) is one of the most commonly used tools in the analysis of ecological data. This method reduces the effective dimensionality of a multivariate data set by producing linear combinations of the original variables (i.e., components) that summarize the predominant patterns in the data. In order to provide meaningful interpretations for principal components, it is important to determine which variables are associated with particular components. Some data analysts incorrectly test the statistical significance of the correlation between original variables and multivariate scores using standard statistical tables. Others interpret eigenvector coefficients larger than an arbitrary absolute value (e.g., 0.50). Resampling, randomization techniques, and parallel analysis have been applied in a few cases. In this study, we compared the performance of a variety of approaches for assessing the significance of eigenvector coefficients in terms of type I error rates and power. Two novel approaches based on the broken-stick model were also evaluated. We used a variety of simulated scenarios to examine the influence of the number of real dimensions in the data; unique versus complex variables; the magnitude of eigenvector coefficients; and the number of variables associated with a particular dimension. Our results revealed that bootstrap confidence intervals and a modified bootstrap confidence interval for the broken-stick model proved to be the most reliable techniques.
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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 | 0.088 | 0.500 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".