Read the fields
| Field | Meaning |
|---|---|
| Eigenvalue | Variance captured by a component on the analysis scale |
| Explained proportion | Component eigenvalue divided by total analyzed variance |
| Cumulative proportion | Variance captured by the retained leading components |
| Loading/rotation | Variable contribution or coefficient, with software convention stated |
| Score | Observation coordinate in component space |
| Communality | Variance represented by retained components under the stated convention |
Scaling changes the analysis. PCA on a covariance matrix gives high-variance variables more influence; PCA on standardized variables analyzes the correlation structure. Report which was used.
A worked component reading
Suppose PC1 explains 42% of standardized variance and has loadings of .71, .68, and .05 on three variables. PC1 mainly contrasts or combines the first two variables, depending on their loading signs; the third contributes little to that component under the software’s loading convention. If PC2 explains another 21%, the first two components explain 63% cumulatively—not 63% of every variable or outcome.
Scores place observations in that component coordinate system. An observation with a high PC1 score expresses more of the variable pattern represented by the positive PC1 direction. Because the sign can flip, “high” only has meaning after the loading orientation is stated.
Signs and rotations
Component signs are arbitrary: multiplying every loading and score on a component by −1 represents the same solution. Interpret relative signs and patterns, not the direction label alone.
Rotation can improve interpretability but changes the loading pattern and, for oblique rotations, component/factor relationships. PCA components are not automatically latent causes.
Common reading errors
- Treating loadings as ordinary regression coefficients without checking convention.
- Comparing a covariance-matrix PCA with a correlation-matrix PCA as if scaling matched.
- Calling a component a real-world construct from one large loading.
- Using cumulative variance alone to decide retention.
- Forgetting that missing-data handling can change the analyzed sample and matrix.
Correlation matrices show the input association structure; reliability output answers a different measurement question.
Retention is not one-rule automation
Scree plots, parallel analysis, cross-validation, domain interpretability, and downstream performance can suggest different retained dimensions. The eigenvalue-greater-than-one rule applies only in particular standardized settings and is not a universal law. Because its primary locator is not part of this package, no numeric retention threshold is promoted.
A defensible reporting sentence
“PCA of standardized variables retained three components explaining 68% cumulatively. Loadings were interpreted by pattern and domain meaning; signs were treated as arbitrary and no universal loading cutoff determined retention.”