R–Data Exploration

PCA

Principal Components Analysis (PCA) allows us to study and
explore a set of quantitative variables measured on a set of objects

Core Idea

 

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
  • ETC
image

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?

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