Principal Components Analysis (PCA) allows us to study and explore a set of quantitative variables measured on a set of objects
With PCA we seek to reduce the dimensionality (reduce the number of variables) of a data set while retaining as much as possible of the variation present in the data
Before performing a PCA(or any other multivariate method) we should start with some preliminary explorations
- Descriptive statistics
- Basic graphical displays
- Distribution of variables
- Pair-wise correlations among variables
- Perhaps transforming some variables
The minimal output from any PCA should contain 3 things:
Eigenvalues provide information about the amount of variability captured by each principal component
Scores or PCs (principal components) that provide coordinates to graphically represent objects in a lower dimensional space
Loadings provide information to determine what variables characterize each principal component
Some questions to keep in mind
- How many PCs should be retained?
- How good (or bad) is the data approximation with the retained PCs?
- What variables characterize each PC?
- Which variables are influential, and how are they correlated?
- Which variables are responsible for the patterns among objects?
- Are there any outlier objects?