14 Principal components and factor analysis


This chapter covers

  • Principal components analysis
  • Exploratory factor analysis
  • Understanding other latent variable models

One of the most challenging aspects of multivariate data is the sheer complexity of the information. If you have a dataset with 100 variables, how do you make sense of all the interrelationships present? Even with 20 variables, there are 190 pairwise correlations to consider when you’re trying to understand how the individual variables relate to one another. Two related but distinct methodologies for exploring and simplifying complex multivariate data are principal components and exploratory factor analysis.

Principal components analysis (PCA) is a data-reduction technique that transforms a larger number of correlated variables into a much smaller set of uncorrelated variables called principal components. For example, you might use PCA to transform 30 correlated (and possibly redundant) environmental variables into 5 uncorrelated composite variables that retain as much information from the original set of variables as possible.

14.1 Principal components and factor analysis in R

14.2 Principal components

14.2.1 Selecting the number of components to extract

14.2.2 Extracting principal components

14.2.3 Rotating principal components

14.2.4 Obtaining principal component scores

14.3 Exploratory factor analysis

14.3.1 Deciding how many common factors to extract

14.3.2 Extracting common factors

14.3.3 Rotating factors

14.3.4 Factor scores

14.3.5 Other EFA-related packages

14.4 Other latent variable models