Instability of statistical factor analysis
Steven P. Ellis · Proceedings of the American Mathematical Society · 2004
Factor analysis, a popular method for interpreting multivariate data, models the covariance among p p variables as being due to a small number ( k k , 1 ≤ k > p 1 \leq k > p ) of hidden variables. A factor analysis of Y Y can be thought of as an ordered or unordered collection, F ( Y ) F(Y) , of k k linearly independent lines in R p \mathbb {R}^{p} . Let Y ′ \mathcal {Y}’ be the collection of data sets for which F ( Y ) F(Y) is defined. The “singularities” of F F are those data sets, Y Y , in the closure, Y ¯ ′ \overline {\mathcal {Y}}’ , at which the limit, lim Y ′ → Y , Y ′ ∈ Y