Principal Components Analysis — principal_components

Function for running a principal components analysis (PCA) with training (and test) data. Expands on the stats::prcomp function.

principal_components_analysis(train, test = NULL)

Arguments

train: A data frame or matrix. Assumes all columns should be included in the PCA.
test: An optional data frame or matrix. Must have the same number of columns and same column names as train.

Value

A list with the standardized data, the results of the call to stats::prcomp, the rotation matrix (eigenvectors), the eigenvalues, the correlations between raw scores and component scores, and the root-mean square error for the training and test sets when using a smaller number of components.

Examples

# Simulate training and test data
train <- MASS::mvrnorm( 100, rep( 0, 8 ), diag(8) )
test <- MASS::mvrnorm( 100, rep( 0, 8 ), diag(8) )

PCA <- principal_components_analysis(
  train = train, test = test
)

# Loading matrix
lambda <- cbind(
  c( runif( 4, .3, .9 ), rep( 0, 4 ) ),
  c( rep( 0, 4 ), runif( 4, .3, .9 ) )
)
# Communalities
D_tau <- diag( runif( 8, .5, 1.5 ) )

cov_mat <- lambda %*% t( lambda ) + D_tau
cor_mat <- cov2cor( cov_mat )

set.seed( 341 ) # For reproducibility
x <- MASS::mvrnorm( n = 200, mu = rep( 0, 8 ), Sigma = cor_mat )
colnames(x) <- paste0( 'C', 1:8 )

PCA <- principal_components_analysis(
  train = x
)