Principal Component Analysis (PCA)

  • PCA is a data reduction procedure, deriving a relatively small number of components that can account for the variability found in a large number of measured response.
  • The 1st principal component captures the maximum variation in the data set. The 2nd principal component has the next most variation, and so on.
  • Principal components do not decompose the variance in the measured responses into common and unique factors as do the factor analysis.
The Analysis Output

The analysis output can include:

  • Correlation or covariance matrix (depending on the selected analysis option)
  • Bartlett's test of sphericity
  • Partial coefficient matrix
  • Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy
  • Eigenvalues (i.e., the proportion of each variable's variance that can be explained by the principal components)
  • PC loadings (eigenvectors)
  • PC scores

Example output from principal component of a dataset that is distributed with both full version and demo version of the application:

Graphs Plotted From Generated PC Scores

PCA: PC Loadings

PCA: Sampling Adequecy

Correlation Matrices and Bartlett's Test of Sphericity

PCA: Correlation Matrix

PCA: Partial Correlation

PCA: Sphericity Test

Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy

Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy includes:

  • Overall measure of sampling adequacy (i.e., a summary for overall variables)
  • Measures of sampling adequacy for individual variables

For the data set to be suitable for PCA analysis, the overall KOM should be above 0.50, and the Bartlett's test of sphericity should be significant

PCA: Sampling Adequecy

Eigenvalues and PC Loadings

PCA: Eigenvalues

PCA: PC Loadings