I want to apply a PCA on a dataset, which consists of mixed type variables (continuous and binary). To illustrate the procedure, I paste a minimal reproducible example in R below.
# Generate synthetic dataset set.seed(12345) n <- 100 x1 <- rnorm(n) x2 <- runif(n, -2, 2) x3 <- x1 + x2 + rnorm(n) x4 <- rbinom(n, 1, 0.5) x5 <- rbinom(n, 1, 0.6) data <- data.frame(x1, x2, x3, x4, x5) # Correlation matrix with appropriate coefficients # Pearson product-moment: 2 continuous variables # Point-biserial: 1 continuous and 1 binary variable # Phi: 2 binary variables # For testing purposes use hetcor function library(polycor) C <- as.matrix(hetcor(data=data)) # Run PCA pca <- princomp(covmat=C) L <- loadings(pca)
Now, I wonder how to calculate component scores (i.e., raw variables weighted by component loadings). When dataset consists of continuous variables, component scores are simply obtained by multiplying (scaled) raw data and eigenvectors stored in loading matrix (L in the example above). Any pointers would be greatly appreciated.