Principal component analysis
Compress measured variation into orthogonal components
Principal component analysis creates orthogonal linear combinations that successively capture the largest remaining variance. It is a descriptive dimension-reduction method, not a latent common-factor model. Centre and scale choices change the result, especially with mixed units. Component scores and loadings help visualise structure but require external interpretation.
Use to summarise many correlated numeric variables, visualise a dataset or prepare a compact representation. Decide whether variance or standardised correlation is the relevant basis and guard against leakage in prediction.
Strengths
- Provides a reproducible low-dimensional summary
- Helps visualise dominant multivariate patterns
Limitations
- High variance need not be substantively important
- Scaling and outliers can dominate components
Know the boundary
PCA scores are weighted combinations of the original measured variables, not automatically psychological constructs or causal factors.