PCA / FA Bartholomew et al.: discussion

This is the 4th post in the Bartholomew et al. sequence in PCA/FA, but it’s an overview of what I did last time. Before we plunge ahead with another set of computations, let me talk about things.

I want to elaborate on the previous post. We discussed

  • the choice of data corresponding to an eigendecomposition of the correlation matrix
  • the pesky \sqrt{N-1} that shows up when we relate the \sqrt{\text{eigenvalues}},\ \Lambda, of a correlation matrix to the principal values w of the standardized data
  • the computation of scores as \sqrt{N-1}\ u
  • the computation of scores as F^T\ where X^T = Z = A\ F
  • the computation of scores as projections of the data onto the reciprocal basis
  • different factorings of the data matrix as scores times loadings

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